Relevant bibliographies by topics / Fractional differential equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Fractional differential equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Fractional differential equation"

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Widad, R. Khudair. "On Solving Comfortable Fractional Differential Equations." Journal of Progressive Research in Mathematics 12, no. 5 (2017): 2073–79. https://doi.org/10.5281/zenodo.3974845.

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This paper adopts the relationship between conformable fractional derivative and the classical derivative. By using this relation, the comfortable fractional differential equation can transform to a classical differential equation such that the solution of these differential equations is the same. Two examples have been considered to illustrate the validity of our main results.
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Pandir, Yusuf, Yusuf Gurefe, and Emine Misirli. "The Extended Trial Equation Method for Some Time Fractional Differential Equations." Discrete Dynamics in Nature and Society 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/491359.

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Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the fractional partial differential equation can be turned into the nonlinear nonfractional ordinary differential equation. For illustrating the reliability of this approach, we apply it to the generalized third order fractional KdV equation and the fractionalKn,nequation according to the complete discrimination system for polynomial method. As a resul
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Albuohimad, Basim. "Exact solution of some fractional integral differential equations by using S-transform." Journal of Interdisciplinary Mathematics 28, no. 3-A (2025): 823–30. https://doi.org/10.47974/jim-1979.

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In this work, we studied fractional differential equations (FDE), which are the differentials of non-integer order. We also discussed the integral differential equations (IDE). By connecting (FDE) and (IDE), a fractional integral differential equation (FIDE) is formed. This research aims to apply the Shehu transform (Տ-transform) to solve this type of linear fractional integral differential equation. The Տ-transform is a powerful tool in math and engineering. This will permit us to convert (FIDE) to algebraic equations, and then by solving this equation, we can acquire the unknown function uti
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Çenesiz, Y., and A. Kurt. "New Fractional Complex Transform for Conformable Fractional Partial Differential Equations." Journal of Applied Mathematics, Statistics and Informatics 12, no. 2 (2016): 41–47. http://dx.doi.org/10.1515/jamsi-2016-0007.

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Abstract Conformable fractional complex transform is introduced in this paper for converting fractional partial differential equations to ordinary differential equations. Hence analytical methods in advanced calculus can be used to solve these equations. Conformable fractional complex transform is implemented to fractional partial differential equations such as space fractional advection diffusion equation and space fractional telegraph equation to obtain the exact solutions of these equations.
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Iskandarova, Gulistan, and Dogan Kaya. "Symmetry solution on fractional equation." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 7, no. 3 (2017): 255–59. http://dx.doi.org/10.11121/ijocta.01.2017.00498.

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As we know nearly all physical, chemical, and biological processes in nature can be described or modeled by dint of a differential equation or a system of differential equations, an integral equation or an integro-differential equation. The differential equations can be ordinary or partial, linear or nonlinear. So, we concentrate our attention in problem that can be presented in terms of a differential equation with fractional derivative. Our research in this work is to use symmetry transformation method and its analysis to search exact solutions to nonlinear fractional partial differential eq
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Güner, Özkan, and Adem C. Cevikel. "A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/489495.

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We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.
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Prakash, Amit, and Hardish Kaur. "An efficient hybrid computational technique for solving nonlinear local fractional partial differential equations arising in fractal media." Nonlinear Engineering 7, no. 3 (2018): 229–35. http://dx.doi.org/10.1515/nleng-2017-0100.

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AbstractIn present work, nonlinear fractional partial differential equations namely transport equation and Fokker-Planck equation involving local fractional differential operators, are investigated by means of the local fractional homotopy perturbation Sumudu transform method. The proposed method is a coupling of homotopy perturbation method with local fractional Sumudu transform and is used to describe the non-differentiable problems. Numerical simulation results are projected to show the efficiency of the proposed technique.
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Muhammad Irfan, Ambreen Bano, Zohaib Sagheer, Sajid Khan, and Muhammad Zubair. "Some New Exact Solutions of The Space Time Boussinesq and Kdv Fractional Partial Differential Equation." Annual Methodological Archive Research Review 3, no. 4 (2025): 50–60. https://doi.org/10.63075/hjqq7p49.

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In this paper, the Modified Riemann-Liouville derivative is proposed to solve Space Time Boussinesq Fractional Partial Differential Equation, and Jumarie’s modified Riemann Liouville derivative is used to convert nonlinear partial fractional differential equation to nonlinear ordinary differential equations. The modified Kudryashov method is applied to compute an approximation to the solutions Of the Space Time Boussinesq Fractional Partial Differential Equation and some Solutions of Space Time Korteweg–de Vries Fractional Partial Differential Equations. As a result, many exact solutions of fr
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Kılıçman, Adem, and Wasan Ajeel Ahmood. "On matrix fractional differential equations." Advances in Mechanical Engineering 9, no. 1 (2017): 168781401668335. http://dx.doi.org/10.1177/1687814016683359.

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The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fracti
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Yakar, Coşkun. "Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference." Abstract and Applied Analysis 2010 (2010): 1–16. http://dx.doi.org/10.1155/2010/762857.

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The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the classical notion of stability to the notion of initial time difference stability for fractional-order differential equations in Caputo's sense. We present a comparison result which again gives the null solution a central role in the comparison fractional-order differential equation when establishing initial tim
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Dissertations / Theses on the topic "Fractional differential equation"

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Tapdigoglu, Ramiz. "Inverse problems for fractional order differential equations." Thesis, La Rochelle, 2019. http://www.theses.fr/2019LAROS004/document.

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Dans cette thèse, nous nous intéressons à résoudre certains problèmes inverses pour des équations différentielles aux dérivées fractionnaires. Un problème inverse est généralement mal posé. Un problème mal posé est un problème qui ne répond pas à l’un des trois critères de Hadamard pour être bien posé, c’est-à-dire, soit l’existence, l’unicité ou une dépendance continue aux données n'est plus vraie, à savoir, des petits changements dans les données de mesure entraînent des changements indéfiniment importants dans la solution. La plupart des difficultés à résoudre des problèmes mal posés sont c
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Hu, Ke. "On an equation being a fractional differential equation with respect to time and a pseudo-differential equation with respect to space related to Lévy-type processes." Thesis, Swansea University, 2012. https://cronfa.swan.ac.uk/Record/cronfa43021.

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Ito, Yu. "Rough path theory via fractional calculus." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199445.

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Grecksch, Wilfried, and Christian Roth. "Approximation of a Quasilinear Stochastic Partial Differential Equation driven by Fractional White Noise." Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800521.

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We approximate the solution of a quasilinear stochastic partial differential equa- tion driven by fractional Brownian motion B_H(t); H in (0,1), which was calculated via fractional White Noise calculus, see [5].
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Agarwal, Divyanshu. "A Study on the Feasibility of Using Fractional Differential Equations for Roll Damping Models." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/52959.

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An optimization algorithm has been developed to study the effectiveness of substituting time tested ODEs with FDEs as applied to ship motions, specifically with an eye toward modeling different forms of roll damping. Relations between the order of differentiation a and damping coefficient b in the FDEs have been drawn for changing damping, added moment of inertia, and initial roll angle. A pitch model has also been studied and compared to the roll model. The error at each of these a and b pairs has also been calculated using an L2-norm. An initial effort was made to correlate the FDE coefficie
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Nguyen, Cu Ngoc. "Stochastic differential equations with long-memory input." Thesis, Queensland University of Technology, 2001.

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Al-Saadony, Muhannad. "Bayesian stochastic differential equation modelling with application to finance." Thesis, University of Plymouth, 2013. http://hdl.handle.net/10026.1/1530.

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In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework. We describe sequential importance sampling, the particle filter and the auxiliary particle filter. We apply these inference methods to the Vasicek Interest Rate model and the standard stochastic volatility model, both to sample from the posterior distribution of the underlying processes and
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Kisela, Tomáš. "Zlomkové diferenciální rovnice a jejich aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2008. http://www.nusl.cz/ntk/nusl-227885.

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Zlomkový kalkulus je matematická disciplína zabývající se vlastnostmi derivací a integrálů neceločíselných řádů (nazývaných zlomkové derivace a integrály, zkráceně diferintegrály) a metodami řešení diferenciálních rovnic obsahujících zlomkové derivace neznámé funkce (tzv. zlomkovými diferenciálními rovnicemi). V této práci představujeme standardní přístupy k definicím zlomkového kalkulu a důkazy některých základních vlastností diferintegrálů. Dále uvádíme krátký přehled metod řešení některých lineárních zlomkových diferenciálních rovnic a vymezujeme hranice jejich použitelnosti. Na závěr si vš
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Zemčíková, Michaela. "Kvalitativní a numerická analýza zlomkových diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2013. http://www.nusl.cz/ntk/nusl-230944.

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This master's thesis deals with fractional differential equations. One of the aims of this thesis is to mention summary of basic types of fractional differential equations. It is very difficult to find their exact solution, hence we will analyze the main qualitative properties of solution, which are stability and asymptotics. Part of the text will be devoted to fractional difference equations, i.e. discussion of numerical solution. At the end of thesis the Bagley-Torvik model will be described with respect to qualitative properties and numerical solution.
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Abdelsheed, Ismail Gad Ameen. "Fractional calculus: numerical methods and SIR models." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3422267.

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Fractional calculus is ”the theory of integrals and derivatives of arbitrary order, which unify and generalize the notions of integer-order differentiation and n-fold integration”. The idea of generalizing differential operators to a non-integer order, in particular to the order 1/2, first appears in the correspondence of Leibniz with L’Hopital (1695), Johann Bernoulli (1695), and John Wallis (1697) as a mere question or maybe even play of thoughts. In the following three hundred years a lot of mathematicians contributed to the fractional calculus: Laplace (1812), Lacroix (1812), Fourier (1822
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Books on the topic "Fractional differential equation"

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Hartley, T. T. A solution to the fundamental linear fractional order differential equation. National Aeronautics and Space Administration, Lewis Research Center, 1998.

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Kochubei, Anatoly, and Yuri Luchko, eds. Fractional Differential Equations. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571660.

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Jin, Bangti. Fractional Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76043-4.

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Benchohra, Mouffak, Erdal Karapınar, Jamal Eddine Lazreg, and Abdelkrim Salim. Fractional Differential Equations. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-34877-8.

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Cardone, Angelamaria, Marco Donatelli, Fabio Durastante, Roberto Garrappa, Mariarosa Mazza, and Marina Popolizio, eds. Fractional Differential Equations. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-7716-9.

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Daftardar-Gejji, Varsha, ed. Fractional Calculus and Fractional Differential Equations. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-9227-6.

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Atangana, Abdon, and Seda İgret Araz. Fractional Stochastic Differential Equations. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0729-6.

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Kubica, Adam, Katarzyna Ryszewska, and Masahiro Yamamoto. Time-Fractional Differential Equations. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-9066-5.

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Milici, Constantin, Gheorghe Drăgănescu, and J. Tenreiro Machado. Introduction to Fractional Differential Equations. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-00895-6.

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Abbas, Saïd, Mouffak Benchohra, and Gaston M. N'Guérékata. Topics in Fractional Differential Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4036-9.

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Book chapters on the topic "Fractional differential equation"

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Ceretani, Andrea, Federico Falcini, and Roberto Garra. "Exact Solutions for the Fractional Nonlinear Boussinesq Equation." In Fractional Differential Equations. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-7716-9_2.

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Kemppainen, Jukka. "Layer potentials for the time-fractional diffusion equation." In Fractional Differential Equations, edited by Anatoly Kochubei and Yuri Luchko. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571660-009.

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Pellegrino, Sabrina Francesca. "A Convolution-Based Method for an Integro-Differential Equation in Mechanics." In Fractional Differential Equations. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-7716-9_7.

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Atanacković, Teodor M., Sanja Konjik, and Stevan Pilipović. "Wave equation involving fractional derivatives of real and complex fractional order." In Fractional Differential Equations, edited by Anatoly Kochubei and Yuri Luchko. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110571660-015.

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Das, Shantanu. "Solution of Generalized Differential Equation Systems." In Functional Fractional Calculus. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20545-3_11.

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Atangana, Abdon, and Seda İgret Araz. "Numerical Scheme for a General Stochastic Equation with Classical and Fractional Derivatives." In Fractional Stochastic Differential Equations. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0729-6_4.

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Owolabi, Kolade M., and Abdon Atangana. "Application to Partial Fractional Differential Equation." In Numerical Methods for Fractional Differentiation. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0098-5_8.

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Atangana, Abdon, and Seda İgret Araz. "Modeling the Spread of Covid-19 with a "Equation missing" Approach: Inclusion of Unreported Infected Class." In Fractional Stochastic Differential Equations. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0729-6_8.

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Otárola, Enrique, and Abner J. Salgado. "Optimization of a Fractional Differential Equation." In Frontiers in PDE-Constrained Optimization. Springer New York, 2018. http://dx.doi.org/10.1007/978-1-4939-8636-1_8.

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Achar, B. N. Narahari, Carl F. Lorenzo, and Tom T. Hartley. "The Caputo Fractional Derivative: Initialization Issues Relative to Fractional Differential Equation." In Advances in Fractional Calculus. Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-6042-7_3.

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Conference papers on the topic "Fractional differential equation"

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"SOLUTION OF THE FUNDAMENTAL LINEAR FRACTIONAL ORDER DIFFERENTIAL EQUATION." In Fractional Order Systems. SciTePress - Science and and Technology Publications, 2007. http://dx.doi.org/10.5220/0001634004070413.

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Bekir, Ahmet, Esin Aksoy, and Özkan Güner. "A generalized fractional sub-equation method for nonlinear fractional differential equations." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893808.

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Sharma, Dharmendra, Saroj Kumar Chandra, and Manish Kumar Bajpai. "Image Enhancement Using Fractional Partial Differential Equation." In 2019 Second International Conference on Advanced Computational and Communication Paradigms (ICACCP). IEEE, 2019. http://dx.doi.org/10.1109/icaccp.2019.8882979.

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Sowa, Marcin, Aleksandra Kawala-Janik, and Waldemar Bauer. "Fractional Differential Equation Solvers in Octave/Matlab." In 2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR). IEEE, 2018. http://dx.doi.org/10.1109/mmar.2018.8485964.

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Dababneh, Amer, Bilal Albarmawi, Marmon Abu Hammad, Amjed Zraiqat, and Tareq Hamadneh. "Conformable Fractional Bernoulli Differential Equation with Applications." In 2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology (JEEIT). IEEE, 2019. http://dx.doi.org/10.1109/jeeit.2019.8717456.

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Malesza, Wiktor, Dominik Sierociuk, and Michal Macias. "Solution of fractional variable order differential equation." In 2015 American Control Conference (ACC). IEEE, 2015. http://dx.doi.org/10.1109/acc.2015.7170951.

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Li, Changpin, and Li Ma. "Well-Posedness of Fractional Differential Equations." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67099.

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Generally speaking, definite conditions of fractional differential equations with Riemann-Liouville, Riesz or Hadamard fractional derivatives are quite different from those of classic differential equations. In this paper, we propose the well-posed conditions for fractional differential equation involving right Riemann-Liouville, Riesz and Hadamard fractional derivatives.
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Boutiara, Abdelatif, Maamar Benbachir, and Kaddour Guerbati. "Caputo type Fractional Differential Equation with Katugampola fractional integral conditions." In 2020 2nd International Conference on Mathematics and Information Technology (ICMIT). IEEE, 2020. http://dx.doi.org/10.1109/icmit47780.2020.9047005.

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Abuualshaikh, Ammar, Farah Aini Abdullah, and M. Ali Akbar. "Application of New Generalized Differential Transform Method to Solve Riccati Fractional Differential Equation." In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). IEEE, 2023. http://dx.doi.org/10.1109/icfda58234.2023.10153326.

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Chong, Kam Yoon, and John G. O’Hara. "Lie symmetry analysis of a fractional Black-Scholes equation." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125072.

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Reports on the topic "Fractional differential equation"

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Lee, Chihoon. Constrained Stochastic Differential Equations Driven by Fractional Brownian Motions: Stationarity and Parameter Estimation Problems. Defense Technical Information Center, 2013. http://dx.doi.org/10.21236/ada591767.

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Myers, Joseph. Fractional Partial Differential Equations for Conservation Laws and Beyond: Theory, Numerics,and Applications (Summary Technical Report, Sep 2015–Nov 2022). DEVCOM Army Research Laboratory, 2023. http://dx.doi.org/10.21236/ad1204021.

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