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A new approach for space-time fractional partial differential equations by residual power series method

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  • Aylin Bayrak, Mine
  • Demir, Ali

Abstract

In this paper, the approximate analytic solution of any order space-time fractional differential equations is constructed by means of semi-analytical method, named as residual power series method (RPSM). The first step is to reduce space-time fractional differential equation to either a space fractional differential equations or a time fractional differential equations before applying RSPM. The main step is to obtain fractional power series solutions by RSPM. At the final step, it is shown that RPSM is very efficacious, plain and powerful for obtaining the solution of any-order space-time fractional differential equations in the form of fractional power series by illustrative examples.

Suggested Citation

  • Aylin Bayrak, Mine & Demir, Ali, 2018. "A new approach for space-time fractional partial differential equations by residual power series method," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 215-230.
    • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:215-230
    DOI: 10.1016/j.amc.2018.04.032
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    References listed on IDEAS

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    1. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    2. El-Ajou, Ahmad & Abu Arqub, Omar & Al-Smadi, Mohammed, 2015. "A general form of the generalized Taylor’s formula with some applications," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 851-859.
    3. El-Ajou, Ahmad & Abu Arqub, Omar & Momani, Shaher & Baleanu, Dumitru & Alsaedi, Ahmed, 2015. "A novel expansion iterative method for solving linear partial differential equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 119-133.
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    1. Kheybari, Samad, 2021. "Numerical algorithm to Caputo type time–space fractional partial differential equations with variable coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 66-85.
    2. Muhammad Imran Liaqat & Ali Akgül & Hanaa Abu-Zinadah, 2023. "Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method," Mathematics, MDPI, vol. 11(2), pages 1-19, January.

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