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Relevant bibliographies by topics / Fractional integral equation

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Academic literature on the topic 'Fractional integral equation'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Fractional integral equation"

1

Aghili, Arman. "Non-homogeneous impulsive time fractional heat conduction equation." Journal of Numerical Analysis and Approximation Theory 52, no. 1 (2023): 22–33. http://dx.doi.org/10.33993/jnaat521-1316.

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This article provides a concise exposition of the integral transforms and its application to singular integral equation and fractional partial differential equations. The author implemented an analytical technique, the transform method, for solving the boundary value problems of impulsive time fractional heat conduction equation. Integral transforms method is a powerful tool for solving singular integral equations, evaluation of certain integrals involving special functions and solution of partial fractional differential equations. The proposed method is extremely concise, attractive as a math

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TARASOV, VASILY E. "THE FRACTIONAL CHAPMAN–KOLMOGOROV EQUATION." Modern Physics Letters B 21, no. 04 (2007): 163–74. http://dx.doi.org/10.1142/s0217984907012712.

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The Chapman–Kolmogorov equation with fractional integrals is derived. An integral of fractional order is considered as an approximation of the integral on fractal. Fractional integrals can be used to describe the fractal media. Using fractional integrals, the fractional generalization of the Chapman–Kolmogorov equation is obtained. From the fractional Chapman–Kolmogorov equation, the Fokker–Planck equation is derived.

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Mondal, Subhabrata, and B. N. Mandal. "Solution of Abel Integral Equation Using Differential Transform Method." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 1 (2018): 7521–32. http://dx.doi.org/10.24297/jam.v14i1.7172.

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The application of fractional differential transform method, developed for differential equations of fractional order, are extended to derive exact analytical solutions of fractional order Abel integral equations. The fractional integrations are described in the Riemann-Liouville sense and fractional derivatives are described in the Caputo sense. Abel integral equation occurs in the mathematical modeling of various problems in physics, astrophysics, solid mechanics and applied sciences. An analytic technique for solving Abel integral equation of first kind by the proposed method is introduced

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Kosmakova, M. T., S. A. Iskakov, and L. Zh Kasymova. "To solving the fractionally loaded heat equation." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 101, no. 1 (2021): 65–77. http://dx.doi.org/10.31489/2021m1/65-77.

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In this paper we consider a boundary value problem for a fractionally loaded heat equation in the class of continuous functions. Research methods are based on an approach to the study of boundary value problems, based on their reduction to integral equations. The problem is reduced to a Volterra integral equation of the second kind by inverting the differential part. We also carried out a study the limit cases for the fractional derivative order of the term with a load in the heat equation of the boundary value problem. It is shown that the existence and uniqueness of solutions to the integral

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Zhou, Mi, Hengtai Wang, Zhenghua Xu, and Lu Zhang. "The Study of Fractional Quadratic Integral Equations Involves General Fractional Integrals." Fractal and Fractional 9, no. 4 (2025): 249. https://doi.org/10.3390/fractalfract9040249.

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This paper investigates the well-posedness of analytical solutions to fractional quadratic differential equations, which involve generalized fractional integrals with respect to other functions. The nonlinear components f and h depend on spatial variables and the general fractional integral, respectively. We use the operator equation T1ωT2ω+T3ω=ω to investigate the existence of solutions, marking the first study of its kind. Using an auxiliary function and Boyd and Wang’s fixed-point theorem, the uniqueness and continuous dependence of the solution are obtained. In particular, we applied nonli

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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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Qayyum, Mubashir, Sidra Afzal, and Efaza Ahmad. "Fractional Modeling of Non-Newtonian Casson Fluid between Two Parallel Plates." Journal of Mathematics 2023 (March 8, 2023): 1–12. http://dx.doi.org/10.1155/2023/5517617.

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In this manuscript, fractional modeling of non-Newtonian Casson fluid squeezed between two parallel plates is performed under the influence of magneto-hydro-dynamic and Darcian effects. The Casson fluid model is fractionally transformed through mixed similarity transformations. As a result, partial differential equations (PDEs) are transformed to a fractional ordinary differential equation (FODE). In the current modeling, the continuity equation is satisfied while the momentum equation of the integral order Casson fluid is recovered when the fractional parameter is taken as α = 1 . A modified

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Hammad, Hasanen A., Hassen Aydi, and Manuel De la Sen. "Solutions of Fractional Differential Type Equations by Fixed Point Techniques for Multivalued Contractions." Complexity 2021 (February 22, 2021): 1–13. http://dx.doi.org/10.1155/2021/5730853.

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This paper involves extended b − metric versions of a fractional differential equation, a system of fractional differential equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting of an extended b − metric space. Thereafter, by making consequent use of the fixed point technique, short and simple proofs are obtained for solutions of a fractional differential equation, a system of fractional differential equations and a two-dimensional linear Fredholm integral equation.

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Yépez-Martínez, Huitzilin, Ivan O. Sosa, and Juan M. Reyes. "Feng’s First Integral Method Applied to the ZKBBM and the Generalized Fisher Space-Time Fractional Equations." Journal of Applied Mathematics 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/191545.

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The fractional derivatives in the sense of the modified Riemann-Liouville derivative and Feng’s first integral method are employed to obtain the exact solutions of the nonlinear space-time fractional ZKBBM equation and the nonlinear space-time fractional generalized Fisher equation. The power of this manageable method is presented by applying it to the above equations. Our approach provides first integrals in polynomial form with high accuracy. Exact analytical solutions are obtained through establishing first integrals. The present method is efficient and reliable, and it can be used as an al

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Berdyshev, A. S., E. T. Karimov, and N. Akhtaeva. "Boundary Value Problems with Integral Gluing Conditions for Fractional-Order Mixed-Type Equation." International Journal of Differential Equations 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/268465.

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Analogs of the Tricomi and the Gellerstedt problems with integral gluing conditions for mixed parabolic-hyperbolic equation with parameter have been considered. The considered mixed-type equation consists of fractional diffusion and telegraph equation. The Tricomi problem is equivalently reduced to the second-kind Volterra integral equation, which is uniquely solvable. The uniqueness of the Gellerstedt problem is proven by energy integrals' method and the existence by reducing it to the ordinary differential equations. The method of Green functions and properties of integral-differential opera

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Dissertations / Theses on the topic "Fractional integral equation"

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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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Kemppainen, J. (Jukka). "Behaviour of the boundary potentials and boundary integral solution of the time fractional diffusion equation." Doctoral thesis, University of Oulu, 2010. http://urn.fi/urn:isbn:9789514261329.

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Abstract The dissertation considers the time fractional diffusion equation (TFDE) with the Dirichlet boundary condition in the sub-diffusion case, i.e. the order of the time derivative is α ∈ (0,1). In the thesis we have studied the solvability of TFDE by the method of layer potentials. We have shown that both the single layer potential and the double layer potential approaches lead to integral equations which are uniquely solvable. The dissertation consists of four articles and a summary section. The first article presents the solution for the time fractional diffusion equation in terms of

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Nguyen, Cu Ngoc. "Stochastic differential equations with long-memory input." Thesis, Queensland University of Technology, 2001.

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Peat, Rhona Margaret. "Fractional powers of operators and mellin multipliers." Thesis, University of Strathclyde, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366801.

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Farquhar, Megan Elizabeth. "Cardiac modelling with fractional calculus: An efficient computational framework for modelling the propagation of electrical impulses in the heart." Thesis, Queensland University of Technology, 2018. https://eprints.qut.edu.au/120682/1/__qut.edu.au_Documents_StaffHome_StaffGroupH%24_halla_Desktop_Megan_Farquhar_Thesis.pdf.

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Heart failure is one of the most common causes of death in the western world. Many heart problems are linked to disturbances in cardiac electrical activity. Further understanding of how electrical impulses propagate through the heart may lead to new diagnosis and treatment options. Using our novel numerical scheme, we are able to conduct preliminary investigations into the effect of fixed and variable order fractional Laplacian operators for modelling propagation of electrical impulses through the heart. We implement our numerical framework to solve the coupled monodomain, Beeler-Reuter mod

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Catellier, Rémi. "Perturbations irrégulières et systèmes différentiels rugueux." Thesis, Paris 9, 2014. http://www.theses.fr/2014PA090032/document.

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Ce travail, à la frontière de l’analyse et des probabilités, s’intéresse à l’étude de systèmes différentiels a priori mal posés. Nous cherchons, grâce à des techniques issues de la théorie des chemins rugueux et de l’étude trajectorielle des processus stochastiques, à donner un sens à de tels systèmes puis à les résoudre, tout en montrant que les notions proposées ici étendent bien les notions classiques de solutions. Cette thèse se décompose en trois chapitres. Le premier traite des systèmes différentiels ordinaires perturbés additivement par des processus irréguliers éventuellement stochasti

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Valente, Maria Serra. "Stability of non-trivial solutions of stochastic differential equations driven by the fractional Brownian motion." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/18993.

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Mestrado em Mathematical Finance<br>O objectivo desta dissertação é o de generalizar um resultado sobre a estabilidade exponencial de soluções triviais de equações diferenciais estocásticas com movimento Browniano fraccionário, desenvolvido por Garrido-Atienza et al., para soluções não-triviais. São apresentadas noções de cálculo fraccionário, assim como a definição e principias propriedades do movimento Browniano fraccionário. De seguida, um framework para equações diferenciais estocásticas com movimento Browniano fraccionário é definido juntamente com resultados de existência e unicidade de

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Camargo, Rubens de Figueiredo. "Calculo fracionario e aplicações." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307012.

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Orientadores: Edmundo Capelas de Oliveira, Ary Orozimbo Chiacchio<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-12T21:42:46Z (GMT). No. of bitstreams: 1 Camargo_RubensdeFigueiredo_D.pdf: 9956358 bytes, checksum: 45d7b7d76ae44d9b713d341ffc7a1ad5 (MD5) Previous issue date: 2009<br>Resumo: Apresentamos neste trabalho um estudo sistemático e detalhado sobre integrais e derivadas de ordens arbitrárias, o assim chamado cálculo de ordem não-inteira, popularizado com o nome de Cálculo Fraci

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Fernandez, Arran. "Analysis in fractional calculus and asymptotics related to zeta functions." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/284390.

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This thesis presents results in two apparently disparate mathematical fields which can both be examined -- and even united -- by means of pure analysis. Fractional calculus is the study of differentiation and integration to non-integer orders. Dating back to Leibniz, this idea was considered by many great mathematical figures, and in recent decades it has been used to model many real-world systems and processes, but a full development of the mathematical theory remains incomplete. Many techniques for partial differential equations (PDEs) can be extended to fractional PDEs too. Three chapters b

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Gomes, Arianne Vellasco [UNESP]. "Transformadas integrais, modelagem fracionária e o sistema de Lotka-Volterra." Universidade Estadual Paulista (UNESP), 2014. http://hdl.handle.net/11449/108781.

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Made available in DSpace on 2014-08-13T14:50:57Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-02-21Bitstream added on 2014-08-13T17:59:56Z : No. of bitstreams: 1 000768672.pdf: 713902 bytes, checksum: bffc0a4e01880e1ffdb1dcb96c2a05b6 (MD5)<br>Este trabalho trata do Cálculo Fracionário e suas aplicações em problemas biológicos. Nas aplicações nos concentramos no sistema de Lotka-Volterra clássico e fracionário, para depois analisar o controle biológico da praga da cana-de-açúcar. Como trabalho futuro, propomos analisar as aplicações do sistema de Lotka-Volterra fracionário em problem

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Books on the topic "Fractional integral equation"

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Samko, S. G. Integraly i proizvodnye drobnogo pori͡a︡dka i nekotorye ikh prilozhenii͡a︡. "Nauka i tekhnika", 1987.

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A, Kilbas A., and Marichev O. I, eds. Fractional integrals and derivatives: Theory and applications. Gordon and Breach Science Publishers, 1993.

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Abbas, Saīd. Advanced fractional differential and integral equations. Nova Science Publishers, Inc., 2015.

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service), SpringerLink (Online, ed. Fractional Differentiation Inequalities. Springer-Verlag New York, 2009.

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Wiesner, Diane M. Your health, our world: The impact of environmental degradation upon human wellbeing. Prism, 1992.

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Annaby, Mahmoud H. q-Fractional Calculus and Equations. Springer Berlin Heidelberg, 2012.

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Abbas, Saïd. Topics in Fractional Differential Equations. Springer New York, 2012.

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Abbas, Saïd / Benchohra, Mouffak / Graef, John R. / Henderson, Johnny. Implicit Fractional Differential and Integral Equations. Walter de Gruyter Inc., 2018.

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Topics In Fractional Differential Equations. Springer, 2012.

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Graef, John R., Johnny Henderson, Saïd Abbas, and Mouffak Benchohra. Implicit Fractional Differential and Integral Equations: Existence and Stability. de Gruyter GmbH, Walter, 2018.

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Book chapters on the topic "Fractional integral equation"

1

Ferreira, M., and N. Vieira. "Multidimensional Time Fractional Diffusion Equation." In Integral Methods in Science and Engineering, Volume 1. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59384-5_10.

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Elhagary, M. A. "Boundary Integral Equation Formulation for Fractional Order Theory of Thermo-Viscoelasticity." In Topics in Integral and Integro-Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65509-9_6.

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Kemppainen, J., and K. Ruotsalainen. "Boundary Integral Solution of the Time-Fractional Diffusion Equation." In Integral Methods in Science and Engineering, Volume 2. Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4897-8_20.

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Gupta, Vidushi, and Jaydev Dabas. "Fractional Functional Impulsive Differential Equation with Integral Boundary Condition." In Mathematical Analysis and its Applications. Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2485-3_34.

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Dubey, Shweta, and S. Chakraverty. "Homotopy Perturbation Method for Solving Fuzzy Fractional Heat-Conduction Equation." In Advances in Fuzzy Integral and Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73711-5_6.

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Schramm, M., A. C. M. Alvim, B. E. J. Bodmann, M. T. B. Vilhena, and C. Z. Petersen. "The Neutron Point Kinetics Equation: Suppression of Fractional Derivative Effects by Temperature Feedback." In Integral Methods in Science and Engineering. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16727-5_46.

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Tailor, Gomatiben, Vinod Gill, and Ravi Shanker Dubay. "Solution of Nonlinear Fractional Differential Equation Using New Integral Transform Method." In Advances in Mathematical Modelling, Applied Analysis and Computation. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0179-9_36.

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Karimov, Erkinjon, Niyaz Tokmagambetov, and Muzaffar Toshpulatov. "On a Mixed Equation Involving Prabhakar Fractional Order Integral-Differential Operators." In Trends in Mathematics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-42539-4_25.

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Son, Nguyen Thi Kim, Hoang Thi Phuong Thao, Tran Van Bang, and Hoang Viet Long. "Complete Controllability of Fuzzy Fractional Evolutions Equation Under Fréchet Derivative in Linear Correlated Fuzzy Spaces." In Advances in Fuzzy Integral and Differential Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73711-5_3.

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Deuri, Bhuban Chandra, and Anupam Das. "Solvability of fractional integral equation via measure of noncompactness and shifting distance functions." In Advances in Mathematical Analysis and its Applications. Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003330868-11.

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Conference papers on the topic "Fractional integral equation"

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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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Narahari Achar, B. N., and John W. Hanneken. "Response Dynamics in the Continuum Limit of the Lattice Dynamical Theory of Viscoelasticity (Fractional Calculus Approach)." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86218.

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A fractional diffusion-wave equation is derived in the continuum limit of the lattice dynamical equations of motion of a chain of coupled fractional oscillators obtained from the integral equations of motion of a linear chain of simple harmonic oscillators by generalization of the ordinary integrals into ones involving fractional integrals. The set of integral equations of motion pertaining to the chain of coupled fractional oscillators in the continuum limit is solved by using Laplace transforms. The response of the system to impulse and sinusoidal forcing is studied. Numerical applications a

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Amori, Ikram H. "Some Perturbation Problems in The Theory of Fractional Integral Equation." In 2014 Global Summit on Computer & Information Technology (GSCIT). IEEE, 2014. http://dx.doi.org/10.1109/gscit.2014.6970132.

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Selvam, A. George Maria, and S. Britto Jacob. "Stability of nonlinear pantograph fractional differential equation with integral operator." In INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS, COMPUTING AND COMMUNICATION TECHNOLOGIES: (ICAMCCT 2021). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0070754.

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Klimek, Malgorzata, and Om Prakash Agrawal. "Space- and Time-Fractional Legendre-Pearson Diffusion Equation." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12604.

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In this paper we study space- and time-fractional diffusion equations called Fractional Legendre-Pearson Diffusion Equations (FLPDEs) in finite space interval. We define the space fractional part using Fractional Legendre Operators and the time fractional part using Fractional Caputo derivative. We consider both the standard and symmetrized versions of FLPDEs. For both equations, we use the method of integral Legendre transform and inverse integral Legendre transform to solve the two equations. The solutions are given in the form of infinite series containing Legendre polynomials dependent on

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Harrouche, Nesrine, Mohammed Al-Smadi, Nadir Djeddi, and Shaher Momani. "Numerical simulation Of Nonlocal Caputo-Fabrizio Fuzzy Fractional Volterra Integral Equation in Hilbert Space." In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). IEEE, 2023. http://dx.doi.org/10.1109/icfda58234.2023.10153324.

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Yilmazer, Resat, and Serkan Karabulut. "Solutions of the generalized Laguerre differential equation by fractional differ integral." In 7TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5078485.

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Dhanasekaran, P., and Ps Deepa. "Rassias stability of a fractional differential equation with integral boundary conditions." In INTERNATIONAL CONFERENCE ON RECENT TRENDS IN PURE AND APPLIED MATHEMATICS (ICRTPAM-2021). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0104897.

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Achar, B. N. Narahari, Tanya Prozny, and John W. Hanneken. "Linear Chain of Coupled Fractional Oscillators: Response Dynamics and Its Continuum Limit." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35403.

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The standard model of a chain of simple harmonic oscillators of Condensed Matter Physics is generalized to a model of linear chain of coupled fractional oscillators in fractional dynamics. The set of integral equations of motion pertaining to the chain of harmonic oscillators is generalized by taking the integrals to be of arbitrary order according to the methods of fractional calculus to yield the equations of motion of a chain of coupled fractional oscillators. The solution is obtained by using Laplace transforms. The continuum limit of the equations is shown to yield the fractional diffusio

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Ge, Fudong, YangQuan Chen, and Chunhai Kou. "The Adjoint Systems of Time Fractional Diffusion Equations and Their Applications in Controllability Analysis." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46696.

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This paper is devoted to the construction of the adjoint system for the case of time fractional order diffusion equations. We first obtain the equivalent integral equation of the abstract fractional state-space system of both Caputo and Riemann-Liouville type by utilizing the Laplace transform and the semigroup theory. Then the adjoint system of time fractional diffusion equation is introduced and used to analyze the duality relationship between observation and control in a Hilbert space. The new introduced notations can also be used in many fields of modelling and control of real dynamic syst

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