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CAS Picard method for fractional nonlinear differential equation

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  • Saeed, Umer

Abstract

In this paper, a computational method for solving the fractional nonlinear differential equation is introduced. We proposed a method by utilizing the CAS wavelets in conjunction with Picard technique. We call the method as CAS Picard method. The fractional nonlinear differential equations are transformed into a system of discrete fractional differential equations by Picard technique and then transformed into a system of algebraic equations by using the operational matrices of CAS wavelets. The error and supporting analysis of the method are also investigated. The comparison analysis of method with other existing numerical methods is also performed.

Suggested Citation

  • Saeed, Umer, 2017. "CAS Picard method for fractional nonlinear differential equation," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 102-112.
    • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:102-112
    DOI: 10.1016/j.amc.2017.02.044
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    References listed on IDEAS

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    1. Saeed, Umer & ur Rehman, Mujeeb, 2015. "Haar wavelet Picard method for fractional nonlinear partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 310-322.
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    Cited by:

    1. Atanacković, Teodor M. & Janev, Marko & Pilipović, Stevan, 2018. "Non-linear boundary value problems involving Caputo derivatives of complex fractional order," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 326-342.
    2. Usman, Muhammad & Hamid, Muhammad & Liu, Moubin, 2021. "Novel operational matrices-based finite difference/spectral algorithm for a class of time-fractional Burger equation in multidimensions," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Muhammad Ismail & Umer Saeed & Jehad Alzabut & Mujeeb ur Rehman, 2019. "Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method," Mathematics, MDPI, vol. 7(12), pages 1-20, December.
    4. Hamid, Muhammad & Usman, Muhammad & Haq, Rizwan Ul & Tian, Zhenfu, 2021. "A spectral approach to analyze the nonlinear oscillatory fractional-order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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