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Solution of fractional integro-differential equations by using fractional differential transform method

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  • Arikoglu, Aytac
  • Ozkol, Ibrahim

Abstract

In this study, fractional differential transform method (FDTM), which is a semi analytical numerical technique, is extended to solve fractional integro-differential equations of Volterra type. New theorems for the transformation of integral terms having degenerate kernels that never existed before are introduced with their proofs. This implemented new technique is validated by solving and comparing four different examples that exist in the literature. It is observed that, FDTM can be utilized as a powerful and reliable tool for the solution of fractional integro-differential equations.

Suggested Citation

  • Arikoglu, Aytac & Ozkol, Ibrahim, 2009. "Solution of fractional integro-differential equations by using fractional differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 521-529.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:521-529
    DOI: 10.1016/j.chaos.2007.08.001
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    1. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
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    Cited by:

    1. Ruby, & Mandal, Moumita, 2024. "Convergence analysis and numerical implementation of projection methods for solving classical and fractional Volterra integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 889-913.
    2. Wang, Jiao & Xu, Tian-Zhou & Wei, Yan-Qiao & Xie, Jia-Quan, 2018. "Numerical simulation for coupled systems of nonlinear fractional order integro-differential equations via wavelets method," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 36-50.
    3. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
    4. Yulin Zhao & Li Huang & Xuebin Wang & Xianyang Zhu, 2012. "Existence of Solutions for Fractional Integro‐Differential Equation with Multipoint Boundary Value Problem in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Muhammed I. Syam & Qasem M. Al-Mdallal & M. Naim Anwar, 2015. "An Efficient Numerical Algorithm for Solving Fractional Higher‐Order Nonlinear Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    6. Xiulian Shi, 2022. "Spectral Collocation Methods for Fractional Integro‐Differential Equations with Weakly Singular Kernels," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    7. Khudair, Ayad R. & Haddad, S.A.M. & khalaf, Sanaa L., 2017. "Restricted fractional differential transform for solving irrational order fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 81-85.
    8. Haifa Bin Jebreen & Ioannis Dassios, 2022. "On the Wavelet Collocation Method for Solving Fractional Fredholm Integro-Differential Equations," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
    9. Llibre, Jaume & Valls, Clàudia, 2018. "On the global dynamics of a finance model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 1-4.
    10. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    11. Kashkari, Bothayna S.H. & Syam, Muhammed I., 2016. "Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 281-291.

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