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Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets

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  • Rayal, Ashish
  • Ram Verma, Sag

Abstract

In the present paper, a method of using fractional order Legendre wavelets is proposed for solving the pantograph differential equation of the stretched type involved with Caputo fractal-fractional and Atangana-Baleanu fractal-fractional derivatives. The suggested approach is based on the fractal-fractional integral operational matrix of fractional order Legendre wavelets and collocation method. The purpose of this article is to analyze the behavior of the pantograph differential equation of the stretched type under the fractal-fractional operators. Two illustrative numerical examples are taken and the results achieved for these examples with different fractional order and fractal order predict the applicability and efficiency of the suggested method using graphs and tables.

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  • Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304732
    DOI: 10.1016/j.chaos.2020.110076
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    Citations

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    Cited by:

    1. Ashish Rayal & Bhagawati Prasad Joshi & Mukesh Pandey & Delfim F. M. Torres, 2023. "Numerical Investigation of the Fractional Oscillation Equations under the Context of Variable Order Caputo Fractional Derivative via Fractional Order Bernstein Wavelets," Mathematics, MDPI, vol. 11(11), pages 1-22, May.
    2. Heydari, M.H. & Razzaghi, M. & Avazzadeh, Z., 2021. "Orthonormal shifted discrete Chebyshev polynomials: Application for a fractal-fractional version of the coupled Schrödinger-Boussinesq system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Admon, Mohd Rashid & Senu, Norazak & Ahmadian, Ali & Majid, Zanariah Abdul & Salahshour, Soheil, 2024. "A new modern scheme for solving fractal–fractional differential equations based on deep feedforward neural network with multiple hidden layer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 311-333.
    4. Rahimkhani, Parisa & Heydari, Mohammad Hossein, 2023. "Fractional shifted Morgan–Voyce neural networks for solving fractal-fractional pantograph differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    5. Muhammad Imran Asjad & Saif Ur Rehman & Ali Ahmadian & Soheil Salahshour & Mehdi Salimi, 2021. "First Solution of Fractional Bioconvection with Power Law Kernel for a Vertical Surface," Mathematics, MDPI, vol. 9(12), pages 1-18, June.

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