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Numerical solution of nonlinear fractional integro-differential equations with weakly singular kernels via a modification of hat functions

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  • Nemati, S.
  • Lima, P.M.

Abstract

In the present paper, a modification of hat functions (MHFs) has been considered for solving a class of nonlinear fractional integro-differential equations with weakly singular kernels, numerically. The fractional order operational matrix of integration is introduced. We provide an error estimation for the approximation of a function by a series of MHFs. To suggest a numerical method, the main problem is converted to an equivalent Volterra integral equation of the second kind and operational matrices of MHFs are used to reduce the problem to the solution of bivariate polynomial equations. Finally, illustrative examples are provided to confirm the accuracy and validity of the proposed method.

Suggested Citation

  • Nemati, S. & Lima, P.M., 2018. "Numerical solution of nonlinear fractional integro-differential equations with weakly singular kernels via a modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 79-92.
    • Handle: RePEc:eee:apmaco:v:327:y:2018:i:c:p:79-92
    DOI: 10.1016/j.amc.2018.01.030
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    References listed on IDEAS

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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.
    2. Mirzaee, Farshid & Hadadiyan, Elham, 2016. "Numerical solution of Volterra–Fredholm integral equations via modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 110-123.
    3. Wang, Yanxin & Zhu, Li, 2016. "SCW method for solving the fractional integro-differential equations with a weakly singular kernel," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 72-80.
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    1. Atangana, Abdon & Araz, Seda İğret, 2019. "Analysis of a new partial integro-differential equation with mixed fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 257-271.

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