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Статті в журналах з теми "Reduced Differential Transform Method (RDTM)"

Автор: Grafiati

Опубліковано: 7 червня 2025

Оновлено: 2 серпня 2025

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1

Benhammouda, Brahim, Hector Vazquez-Leal, and Arturo Sarmiento-Reyes. "Modified Reduced Differential Transform Method for Partial Differential-Algebraic Equations." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/279481.

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Анотація:

This work presents the application of the reduced differential transform method (RDTM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-two and index-three are solved to show that RDTM can provide analytical solutions for PDAEs in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful technique to find exact solutions. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend

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2

T.R. Ramesh Rao. "A study on linear and non linear Schrodinger equations by reduced differential transform method." Malaya Journal of Matematik 4, no. 01 (2016): 59–64. http://dx.doi.org/10.26637/mjm401/008.

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Анотація:

In this paper, reduced differential transform method (RDTM) is used to obtain the exact solution of nonlinear Schrodinger equation. Compared to other existing analytical/numerical methods, RDTM is more efficient and easy to apply.

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3

Srivastava, Vineet K., Mukesh K. Awasthi, R. K. Chaurasia, and M. Tamsir. "The Telegraph Equation and Its Solution by Reduced Differential Transform Method." Modelling and Simulation in Engineering 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/746351.

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Анотація:

One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM). Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

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4

Tuan, Nguyen Minh. "A Study of Applied Reduced Differential Transform Method Using Volterra Integral Equations in Solving Partial Differential Equations." EQUATIONS 3 (October 3, 2023): 93–103. http://dx.doi.org/10.37394/232021.2023.3.11.

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Анотація:

Nowadays, integration is one of the trending fields applied in calculus, especially in partial differential equations. Researchers are contributing to support useful utilities to solve partial differential equations in many kinds of methods. In this paper, we perform an application of Volterra Integral Equations in a reduced differential transform method (we call VIE-RDTM) to find the approximate solutions of partial differential equations. The aim is to find the approximate solutions approach to the exact solutions with more general forms. We also extend some new results for basic functions a

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5

Cui, Zhoujin, Zisen Mao, Sujuan Yang, and Pinneng Yu. "Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/186934.

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Анотація:

The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the f

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6

Khalid, Aliyu Muhammad1 2. Aliyu Aliyu Isa2 3. Tiwari Sarita1 2. Sylvain Meinrad Donkeng Voumo 4*. "Application of Reduced Differential Transform Method to Solve Linear, Non-Linear Convection-Diffusion and Reaction-Diffusion Problems." MSI Journal of Multidisciplinary Research (MSIJMR) Volume 2, Issue 5 (2025): 55–64. https://doi.org/10.5281/zenodo.15372549.

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Анотація:

Convection-diffusion and reaction-diffusion equations are fundamental in describing various physical phenomena, yet their solution, particularly for nonlinear cases, often presents significant mathematical challenges. This study investigates the application of the Reduced Differential Transform Method (RDTM) to obtain analytical solutions for both linear and nonlinear convection-diffusion and reaction-diffusion problems. The RDTM, derived from power series expansion, was systematically applied to four illustrative examples: two linear convection-diffusion equations and two nonlinear reaction-d

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7

Abdul Rahman Farhan Sabdin, Che Haziqah Che Hussin, Jumat Sulaiman, and Arif Mandangan. "Multistep Reduced Differential Transform Method in Solving Nonlinear Schrodinger Equations." Journal of Advanced Research in Applied Sciences and Engineering Technology 44, no. 2 (2024): 112–23. http://dx.doi.org/10.37934/araset.44.2.112123.

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Анотація:

This paper obtains semi-analytical solutions for the nonlinear Schrodinger equations (NLSEs) using the multistep reduced differential transform method (MsRDTM). The implemented method yields an analytical approximate solution over a longer time frame, in which the method applied is treated as an algorithm in a sequence of small sub-division of intervals of identical length compared to the traditional reduced differential transform method (RDTM). Excluding the need of perturbation, linearization, or discretization, this method offers the benefit and reliability of the multistep algorithm. The o

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8

Abazari, Reza, and Adem Kılıçman. "Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/929478.

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Анотація:

The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM), and compared with the differential transform method (DTM). The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equa

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9

Osman, Mawia, Yonghui Xia, Muhammad Marwan, and Omer Abdalrhman Omer. "Novel Approaches for Solving Fuzzy Fractional Partial Differential Equations." Fractal and Fractional 6, no. 11 (2022): 656. http://dx.doi.org/10.3390/fractalfract6110656.

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Анотація:

In this paper, we present a comparison of several important methods to solve fuzzy partial differential equations (PDEs). These methods include the fuzzy reduced differential transform method (RDTM), fuzzy Adomian decomposition method (ADM), fuzzy Homotopy perturbation method (HPM), and fuzzy Homotopy analysis method (HAM). A distinguishing practical feature of these techniques is administered without the need to use discretion or restricted assumptions. Moreover, we investigate the fuzzy (n+1)-dimensional fractional RDTM to obtain the solutions of fuzzy fractional PDEs. The much more distinct

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10

Arslan, Derya. "The Comparison Study of Hybrid Method with RDTM for Solving Rosenau-Hyman Equation." Applied Mathematics and Nonlinear Sciences 5, no. 1 (2020): 267–74. http://dx.doi.org/10.2478/amns.2020.1.00024.

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Анотація:

AbstractIn this paper, the hybrid method (differential transform and finite difference methods) and the RDTM (reduced differential transform method) are implemented to solve Rosenau-Hyman equation. These methods give the desired accurate results in only a few terms and the approach procedure is rather simple and effective. An experiment is given to demonstrate the efficiency and reliability of these presented methods. The obtained numerical results are compared with each other and with exact solution. It seems that the results of the hybrid method and the RDTM show good performance as the othe

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11

Osman, Mawia, Zengtai Gong, and Altyeb Mohammed Mustafa. "A fuzzy solution of nonlinear partial differential equations." Open Journal of Mathematical Analysis 5, no. 1 (2021): 51–63. http://dx.doi.org/10.30538/psrp-oma2021.0082.

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Анотація:

In this paper, the reduced differential transform method (RDTM) is applied to solve fuzzy nonlinear partial differential equations (PDEs). The solutions are considered as infinite series expansions which converge rapidly to the solutions. Some examples are solved to illustrate the proposed method.

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12

Osman, Mawia, Almegdad Almahi, Omer Abdalrhman Omer, Altyeb Mohammed Mustafa, and Sarmad A. Altaie. "Approximation Solution for Fuzzy Fractional-Order Partial Differential Equations." Fractal and Fractional 6, no. 11 (2022): 646. http://dx.doi.org/10.3390/fractalfract6110646.

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Анотація:

In this article, the authors study the comparison of the generalization differential transform method (DTM) and fuzzy variational iteration method (VIM) applied to determining the approximate analytic solutions of fuzzy fractional KdV, K(2,2) and mKdV equations. Furthermore, we establish the approximation solution two-and three-dimensional fuzzy time-fractional telegraphic equations via the fuzzy reduced differential transform method (RDTM). Finding an exact or closed-approximation solution to a differential equation is possible via fuzzy RDTM. Finally, we present the fuzzy fractional variatio

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13

Zinah Abdulkadhim Hasan and Abdul-Sattar Jaber Ali. "The Comparison Study of the Hybrid Method for Solving the Unsteady State Two-Dimensional Convection-Diffusion Equations." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 99, no. 2 (2022): 67–86. http://dx.doi.org/10.37934/arfmts.99.2.6786.

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In this paper, we present a hybrid method combining the reduced differential transform method (RDTM) and a resumption method based on Yang transform and Padé approximant to find analytical solutions for three test problems for the unsteady state two-dimensional convection-diffusion equation. The proposed method significantly improves the approximate solution series and broadens the convergence field of RDTM. The numerical results obtained are compared to RDTM and other results from previous works. The results show that the proposed method is very efficient and has high accuracy. The main advan

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14

Fadugba, S. E., F. Ali, and A. B. Abubakar. "Caputo fractional reduced differential transform method for SEIR epidemic model with fractional order." Mathematical Modeling and Computing 8, no. 3 (2021): 537–48. http://dx.doi.org/10.23939/mmc2021.03.537.

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Анотація:

This paper proposes the Caputo Fractional Reduced Differential Transform Method (CFRDTM) for Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model with fractional order in a host community. CFRDTM is the combination of the Caputo Fractional Derivative (CFD) and the well-known Reduced Differential Transform Method (RDTM). CFRDTM demonstrates feasible progress and efficiency of operation. The properties of the model were analyzed and investigated. The fractional SEIR epidemic model has been solved via CFRDTM successfully. Hence, CFRDTM provides the solutions of the model in the form of a

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15

Osman, Mawia, Yonghui Xia, Omer Abdalrhman Omer, and Ahmed Hamoud. "On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations." Mathematics 10, no. 13 (2022): 2295. http://dx.doi.org/10.3390/math10132295.

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Анотація:

In this article, we present the fuzzy Adomian decomposition method (ADM) and fuzzy modified Laplace decomposition method (MLDM) to obtain the solutions of fuzzy fractional Navier–Stokes equations in a tube under fuzzy fractional derivatives. We have looked at the turbulent flow of a viscous fluid in a tube, where the velocity field is a function of only one spatial coordinate, in addition to time being one of the dependent variables. Furthermore, we investigate the fuzzy Elzaki transform, and the fuzzy Elzaki decomposition method (EDM) applied to solving fuzzy linear-nonlinear Schrodinger diff

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16

Deresse, Alemayehu Tamirie. "Analytical Solution of One-Dimensional Nonlinear Conformable Fractional Telegraph Equation by Reduced Differential Transform Method." Advances in Mathematical Physics 2022 (July 21, 2022): 1–18. http://dx.doi.org/10.1155/2022/7192231.

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Анотація:

In this paper, the reduced differential transform method (RDTM) is successfully implemented to obtain the analytical solution of the space-time conformable fractional telegraph equation subject to the appropriate initial conditions. The fractional-order derivative will be in the conformable (CFD) sense. Some properties which help us to solve the governing problem using the suggested approach are proven. The proposed method yields an approximate solution in the form of an infinite series that converges to a closed-form solution, which is in many cases the exact solution. This method has the adv

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17

Günerhan, Hatıra. "Analytical and approximate solution of two-dimensional convection-diffusion problems." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 10, no. 1 (2020): 73–77. http://dx.doi.org/10.11121/ijocta.01.2020.00781.

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Анотація:

In this work, we have used reduced differential transform method (RDTM) to compute an approximate solution of the Two-Dimensional Convection-Diffusion equations (TDCDE). This method provides the solution quickly in the form of a convergent series. Also, by using RDTM the approximate solution of two-dimensional convection-diffusion equation is obtained. Further, we have computed exact solution of non-homogeneous CDE by using the same method. To the best of my knowledge, the research work carried out in the present paper has not been done, and is new. Examples are provided to support our work.

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18

Al-Saif, A. S. J., and Zinah A. Hasan. "An analytical approximate method for solving unsteady state two-dimensional convection-diffusion equations." JOURNAL OF ADVANCES IN MATHEMATICS 21 (June 22, 2022): 73–88. http://dx.doi.org/10.24297/jam.v21i.9242.

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Анотація:

In this paper, an analytic approximate method for solving the unsteady two-dimensional convection-diffusion equations is introduced. Also, the convergence of the approximate methods is analyzed. Three test examples are presented, two have exact and one has not exacted solutions. The results obtained show that these methods are powerful mathematical tools for solving linear and nonlinear partial differential equations, moreover, new analytic Taylor method (NATM), reduced differential transform method (RDTM), and homotopy perturbation method (HPM), are more accurate and have less CPU time than t

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19

Gusu, Daba Meshesha, Dechasa Wegi, Girma Gemechu, and Diriba Gemechu. "Fractional Order Airy’s Type Differential Equations of Its Models Using RDTM." Mathematical Problems in Engineering 2021 (September 10, 2021): 1–21. http://dx.doi.org/10.1155/2021/3719206.

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Анотація:

In this paper, we propose a novel reduced differential transform method (RDTM) to compute analytical and semianalytical approximate solutions of fractional order Airy’s ordinary differential equations and fractional order Airy’s and Airy’s type partial differential equations subjected to certain initial conditions. The performance of the proposed method was analyzed and compared with a convergent series solution form with easily computable coefficients. The behavior of approximated series solutions at different values of fractional order α and its modeling in 2-dimensional and 3-dimensional sp

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20

Belayeh, Wayinhareg Gashaw, Yesuf Obsie Mussa, and Ademe Kebede Gizaw. "Approximate Analytic Solutions of Two-Dimensional Nonlinear Klein–Gordon Equation by Using the Reduced Differential Transform Method." Mathematical Problems in Engineering 2020 (December 15, 2020): 1–12. http://dx.doi.org/10.1155/2020/5753974.

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Анотація:

In this paper, the reduced differential transform method (RDTM) is successfully implemented for solving two-dimensional nonlinear Klein–Gordon equations (NLKGEs) with quadratic and cubic nonlinearities subject to appropriate initial conditions. The proposed technique has the advantage of producing an analytical approximation in a convergent power series form with a reduced number of calculable terms. Two test examples from mathematical physics are discussed to illustrate the validity and efficiency of the method. In addition, numerical solutions of the test examples are presented graphically t

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21

Deresse, Alemayehu Tamirie, Yesuf Obsie Mussa, and Ademe Kebede Gizaw. "Approximate Analytical Solution of Two-Dimensional Nonlinear Time-Fractional Damped Wave Equation in the Caputo Fractional Derivative Operator." Mathematical Problems in Engineering 2022 (November 4, 2022): 1–28. http://dx.doi.org/10.1155/2022/7004412.

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Анотація:

In this work, we proposed a new method called Laplace–Padé–Caputo fractional reduced differential transform method (LPCFRDTM) for solving a two-dimensional nonlinear time-fractional damped wave equation subject to the appropriate initial conditions arising in various physical models. LPCFRDTM is the amalgamation of the Laplace transform method (LTM), Padé approximant, and the well-known reduced differential transform method (RDTM) in the Caputo fractional derivative senses. First, the solution to the problem is gained in the convergent power series form with the help of the Caputo fractional-r

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22

Appadu, Appanah Rao, and Abey Sherif Kelil. "On Semi-Analytical Solutions for Linearized Dispersive KdV Equations." Mathematics 8, no. 10 (2020): 1769. http://dx.doi.org/10.3390/math8101769.

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Анотація:

The most well-known equations both in the theory of nonlinearity and dispersion, KdV equations, have received tremendous attention over the years and have been used as model equations for the advancement of the theory of solitons. In this paper, some semi-analytic methods are applied to solve linearized dispersive KdV equations with homogeneous and inhomogeneous source terms. These methods are the Laplace-Adomian decomposition method (LADM), Homotopy perturbation method (HPM), Bernstein-Laplace-Adomian Method (BALDM), and Reduced Differential Transform Method (RDTM). Three numerical experiment

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23

Sabdin, Abdul Rahman Farhan, Che Haziqah Che Hussin, Jumat Sulaiman, Arif Mandangan, and Essam Roshdy El-Zahar. "An Adaptive Semi-Analytical Approach in Solving Nonlinear Korteweg-De Vries Equations." CFD Letters 17, no. 6 (2024): 107–21. https://doi.org/10.37934/cfdl.17.6.107121.

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Анотація:

This paper introduces a novel method named the Adaptive Hybrid Reduced Differential Transform Method (AHRDTM) for solving Nonlinear Korteweg-De Vries Equations (NKdVEs). AHRDTM provides convergent semi-analytical solutions over long-time frames by generating subintervals of varying lengths, significantly reducing the number of time-steps and processing time needed for solutions, distinguishing it from the traditional multistep approach of RDTM. Notably, AHRDTM avoids the need for perturbation, linearization or discretization, enhancing its adaptability and reliability. The findings demonstrate

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24

Singh, Brajesh Kumar, and Mahendra. "A Numerical Computation of a System of Linear and Nonlinear Time Dependent Partial Differential Equations Using Reduced Differential Transform Method." International Journal of Differential Equations 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/4275389.

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Анотація:

This paper deals with an analytical solution of an initial value system of time dependent linear and nonlinear partial differential equations by implementing reduced differential transform (RDT) method. The effectiveness and the convergence of RDT method are tested by means of five test problems, which indicates the validity and great potential of the reduced differential transform method for solving system of partial differential equations.

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25

Che Haziqah Che Hussin, Amirah Azmi, and Adem Kilicman. "Solitary Wave Solutions with Compact Support for The Nonlinear Dispersive K(m,n) Equations by Using Approximate Analytical Method." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 88, no. 1 (2021): 24–34. http://dx.doi.org/10.37934/arfmts.88.1.2434.

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Анотація:

The study of solitons and compactons is important in nonlinear physics. In this paper we combined the Adomian polynomials with the multi-step approach to present a new technique called Multi-step Modified Reduced Differential Transform Method (MMRDTM). The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with a reduced number of calculated terms. The MMRDTM is presented with some modification of the Reduced Differential Transformation Method (RDTM) with multi-step approach and its nonlinear term is replaced by the Adomian polynomials.

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26

Abaid Ur Rehman, Muhammad, Jamshad Ahmad, Ali Hassan, et al. "The Dynamics of a Fractional-Order Mathematical Model of Cancer Tumor Disease." Symmetry 14, no. 8 (2022): 1694. http://dx.doi.org/10.3390/sym14081694.

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Анотація:

This article explores the application of the reduced differential transform method (RDTM) for the computational solutions of two fractional-order cancer tumor models in the Caputo sense: the model based on cancer chemotherapeutic effects which explain the relation between chemotherapeutic drugs, tumor cells, normal cells, and immune cells using a fractional partial differential equations, and the model that describes the different cases of killing rate K of cancer cells (the killing percentage of cancer cells K (I) is dependent on the number of cells, (II) is a function of time only, and (III)

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27

Deresse, Alemayehu Tamirie, Yesuf Obsie Mussa, and Ademe Kebede Gizaw. "Analytical Solution of Two-Dimensional Sine-Gordon Equation." Advances in Mathematical Physics 2021 (May 1, 2021): 1–15. http://dx.doi.org/10.1155/2021/6610021.

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Анотація:

In this paper, the reduced differential transform method (RDTM) is successfully implemented for solving two-dimensional nonlinear sine-Gordon equations subject to appropriate initial conditions. Some lemmas which help us to solve the governing problem using the proposed method are proved. This scheme has the advantage of generating an analytical approximate solution or exact solution in a convergent power series form with conveniently determinable components. The method considers the use of the appropriate initial conditions and finds the solution without any discretization, transformation, or

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28

R.Ramesh Rao, T. "Numerical Solution of Time Fractional Parabolic Differential Equations." International Journal of Engineering & Technology 7, no. 4.10 (2018): 790. http://dx.doi.org/10.14419/ijet.v7i4.10.26117.

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Анотація:

In this paper, we study the coupling of an approximate analytical technique called reduced differential transform (RDT) with fractional complex transform. The present method reduces the time fractional differential equations in to integer order differential equations. The fractional derivatives are defined in Jumaries modified Riemann-Liouville sense. Result shows that the present technique is effective and powerful for handling the fractional order differential equations.

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29

Kumar, Sunil, Surath Ghosh, Shaher Momani, and S. Hadid. "Robotnov function based operator for biological population model of biology." International Journal of Numerical Methods for Heat & Fluid Flow 32, no. 1 (2021): 1–22. http://dx.doi.org/10.1108/hff-09-2020-0570.

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Анотація:

Purpose The population model has an important role in biology to interpret the spreading rate of viruses and parasites. This biological model is also used to identify fragile species. This paper aims to propose a new Yang-Abdel-Aty-Cattani (YAC) fractional operator with a non-singular kernel to solve nonlinear partial differential equation, which is arised in biological population model. Here, this study has explained the analytical methods, reduced differential transform method (RDTM) and residual power series method (RPSM) taking the fractional derivative as YAC operator sense. Design/method

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30

Khan, Khalid, Manuel De la Sen, Muhammad Irfan, and Amir Ali. "Higher Order Non-Planar Electrostatic Solitary Potential in a Streaming Electron-Ion Magnetoplasma: Phase Plane Analysis." Symmetry 15, no. 2 (2023): 436. http://dx.doi.org/10.3390/sym15020436.

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Анотація:

We investigate cylindrical and spherical solitons in electron-ion (EI) plasma that contains hot (cold) electrons with stationary ions. The magneto-hydrodynamic equations are solved with the aid of the reductive perturbation (RP) technique, leading to the modified Korteweg–De Vries (mKdV) equation for the non-linear behaviour of the solitary waves in EI plasma. By employing the reduced differential transform method (RDTM), an approximate solution of the mKdV is obtained for solitary waves. Phase plane analysis reveals that these excitations exhibit periodic oscillations. The phase plane and per

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31

Naseem, Tahir. "Novel techniques for solving Goursat partial differential equations in the linear and nonlinear regime." International Journal of Emerging Multidisciplinaries: Mathematics 1, no. 1 (2022): 17–37. http://dx.doi.org/10.54938/ijemdm.2022.01.1.7.

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Анотація:

The Goursat problem, which is related to hyperbolic partial differential equations, occurs in a variety of branches of physics and engineering. We studied the solution of the Goursat partial differential equation utilizing the reduced differential transform (RDT) and Adomian decomposition (AD) techniques in this inquiry. The problem's analytical solution is found in series form, which converges to exact solutions. The approaches' reliability and efficiency were evaluated using the Goursat problems (linear and non-linear). Additionally, the accuracy of the findings obtained demonstrates the red

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32

Al-Smadi, Mohammed, Asad Freihat, Hammad Khalil, Shaher Momani, and Rahmat Ali Khan. "Numerical Multistep Approach for Solving Fractional Partial Differential Equations." International Journal of Computational Methods 14, no. 03 (2017): 1750029. http://dx.doi.org/10.1142/s0219876217500293.

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Анотація:

In this paper, we proposed a novel analytical technique for one-dimensional fractional heat equations with time fractional derivatives subjected to the appropriate initial condition. This new analytical technique, namely multistep reduced differential transformation method (MRDTM), is a simple amendment of the reduced differential transformation method, in which it is treated as an algorithm in a sequence of small intervals, in order to hold out accurate approximate solutions over a longer time frame compared to the traditional RDTM. The fractional derivatives are described in the Caputo sense

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33

Jain, Pankaj, Chandrani Basu, and Vivek Panwar. "Reduced $pq$-Differential Transform Method and Applications." Journal of Inequalities and Special Functions 13, no. 1 (2022): 24–40. http://dx.doi.org/10.54379/jiasf-2022-1-3.

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Анотація:

In this paper, Reduced Differential Transform method in the framework of (p, q)-calculus, denoted by Rp,qDT , has been introduced and applied in solving a variety of differential equations such as diffusion equation, 2Dwave equation, K-dV equation, Burgers equations and Ito system. While the diffusion equation has been studied for the special case p = 1, i.e., in the framework of q-calculus, the other equations have not been studied even in q-calculus.

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34

Al-Amr, Mohammed O. "New applications of reduced differential transform method." Alexandria Engineering Journal 53, no. 1 (2014): 243–47. http://dx.doi.org/10.1016/j.aej.2014.01.003.

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35

Keskin, Yıldıray, and Galip Oturanç. "Reduced Differential Transform Method for Generalized KdV Equations." Mathematical and Computational Applications 15, no. 3 (2010): 382–93. http://dx.doi.org/10.3390/mca15030382.

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36

Lin, Bin. "REDUCED DIFFERENTIAL TRANSFORM METHOD FOR NONLINEAR SCHRÖDINGER EQUATION." Far East Journal of Dynamical Systems 26, no. 2 (2015): 91–98. http://dx.doi.org/10.17654/fjdsjun2015_091_098.

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37

Düz, M. "Solution of complex differential equations by using reduced differential transform method." Miskolc Mathematical Notes 21, no. 1 (2020): 161. http://dx.doi.org/10.18514/mmn.2020.3240.

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38

Gepree, K. A., A. M. S. Mahdy, M. S. Mohamed, and A. Al-Amiri. "Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models." Computers, Materials & Continua 61, no. 3 (2019): 979–94. http://dx.doi.org/10.32604/cmc.2019.07701.

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39

Teppawar, R. S., R. N. Ingle, and R. A. Muneshwar. "Analysis of system of fractional partial differential equations using Laplace reduced differential transform with decomposition method." Journal of Statistics and Management Systems 27, no. 8 (2024): 1577–94. https://doi.org/10.47974/jsms-1112.

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In this article, we discuss how to solve systems of nonlinear fractional partial differential equations (NFPDEs) by combining the Laplace transform & the reduced differential transform method, often known as the Laplace reduced differential transform with decompostion method (LRDTDM). It is generally considered how to deal with these concerns. In addition, systems of FPDEs of different orders may be solved using this method. The algorithm is Efficient and effective. The convergence and existence results for the suggested technique are presented. To illustrate the reliability and effectiven

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40

Yu, Jianping, Jian Jing, Yongli Sun, and Suping Wu. "(n+1)-Dimensional reduced differential transform method for solving partial differential equations." Applied Mathematics and Computation 273 (January 2016): 697–705. http://dx.doi.org/10.1016/j.amc.2015.10.016.

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41

Moosavi Noori, Seyyedeh Roodabeh, and Nasir Taghizadeh. "Study of Convergence of Reduced Differential Transform Method for Different Classes of Differential Equations." International Journal of Differential Equations 2021 (April 29, 2021): 1–16. http://dx.doi.org/10.1155/2021/6696414.

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In this work, we study the sufficient condition for convergence of the reduced differential transform method for nonlinear differential equations. The main power of this method is its ability and flexibility in solving linear and nonlinear problems properly and easily and obtain solutions both numerically and analytically. Simple approaches of reduced differential transform method and the convergence results for different classes of differential equations such as linear and nonlinear ordinary, partial, fractional, and system of differential equations are briefly discussed. Eight examples are c

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42

Çetınkaya, Süleyman, and Ali Demir. "Effects of the ARA transform method for time fractional problems." Mathematica Moravica 26, no. 2 (2022): 73–84. http://dx.doi.org/10.5937/matmor2202073c.

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The aim of this study is to establish the solutions of time fractional mathematical problems with the aid of new integral transforms called the ARA transform. The fractional derivative is taken in the sense of Liouville-Caputo derivative. The fractional partial differential equations are reduced into ordinary differential equations. Later solving this fractional equation and applying inverse the ARA transform, the solution is acquired. The implementation of this transform for fractional differential equations is very similar to the implementation of the Laplace transform. However, the ARA tran

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43

Haghbin, A., and S. Hesam. "Reduced Differential Transform Method For Solving Seventh Order Sawadakotera Equations." Journal of Mathematics and Computer Science 05, no. 01 (2012): 53–59. http://dx.doi.org/10.22436/jmcs.05.01.06.

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44

Jafari, Hossein, Hassan K. Jassim, Seithuti P. Moshokoa, Vernon M. Ariyan, and Fairouz Tchier. "Reduced differential transform method for partial differential equations within local fractional derivative operators." Advances in Mechanical Engineering 8, no. 4 (2016): 168781401663301. http://dx.doi.org/10.1177/1687814016633013.

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45

Alain Servais Wellot, Yanick. "SOLVING PARTIAL DIFFERENTIAL EQUATIONS MODELLING SURFACE FLOWS BY THE REDUCED DIFFERENTIAL TRANSFORM METHOD." Journal of Computer Science and Applied Mathematics 5, no. 2 (2023): 75–88. http://dx.doi.org/10.37418/jcsam.5.2.3.

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The aim of this work is to find exact solutions of the non-linear partial differential equations describing the motion of Newtonian fluids at the surface. The reduced differential transform method is used to find the exact solutions of these equations. This method produces an algorithm that favours rapid convergence of the problem towards the exact solution sought.

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46

Tuan, Nguyen Minh, Phayung Meesad, and Piwan Wongsashinchai. "A Fractional Reduced Differential Transform Method for Solving Multi-Fractional Telegraph Equations." WSEAS TRANSACTIONS ON ELECTRONICS 15 (November 18, 2024): 97–109. http://dx.doi.org/10.37394/232017.2024.15.12.

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This paper presents a novel modification of the Fractional Reduced Differential Transform Method (FRDTM) to solve space-time multi-fractional telegraph equations. The telegraph equation is crucial in modeling voltage and current distribution in electrical transmission lines, and its solutions have applications in physics, economics, and applied mathematics. The proposed method effectively simplifies the fractional differential equations by omitting one fractional derivative term, allowing for the transformation of the remaining terms using the FRDTM. The solutions demonstrate the method’s accu

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47

Düz, Murat. "Solution of complex differential equations with variable coefficients by using reduced differential transform." Miskolc Mathematical Notes 23, no. 2 (2022): 621. http://dx.doi.org/10.18514/mmn.2022.3442.

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Анотація:

In this article, solution of complex partial derivative equations with variable coefficients from the first and second order have been investigated. For this solution, an iteration relation was obtained using the reduced differential transform method. This method also was been applied for ordinary complex differential equations which examined in the literature. The solution which has been obtained has been seen compatible with the literature.

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48

MEHTI, Giriraj. "Reduced Differential Transform Method for Exact Solution of Parabolic and Hyperbolic Partial Differential Equations." Journal of Applied Computer Science & Mathematics 11, no. 1 (2017): 25–27. http://dx.doi.org/10.4316/jacsm.201701005.

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49

Acan, Omer, Maysaa Mohamed Al Qurashi, and Dumitru Baleanu. "Reduced differential transform method for solving time and space local fractional partial differential equations." Journal of Nonlinear Sciences and Applications 10, no. 10 (2017): 5230–38. http://dx.doi.org/10.22436/jnsa.010.10.09.

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50

Mohamed, Mohamed S., and Khaled A. Gepreel. "Reduced differential transform method for nonlinear integral member of Kadomtsev–Petviashvili hierarchy differential equations." Journal of the Egyptian Mathematical Society 25, no. 1 (2017): 1–7. http://dx.doi.org/10.1016/j.joems.2016.04.007.

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