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An Improved Version of Residual Power Series Method for Space‐Time Fractional Problems

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  • Mine Aylin Bayrak
  • Ali Demir
  • Ebru Ozbilge

Abstract

The task of present research is to establish an enhanced version of residual power series (RPS) technique for the approximate solutions of linear and nonlinear space‐time fractional problems with Dirichlet boundary conditions by introducing new parameter λ. The parameter λ allows us to establish the best numerical solutions for space‐time fractional differential equations (STFDE). Since each problem has different Dirichlet boundary conditions, the best choice of the parameter λ depends on the problem. This is the major contribution of this research. The illustrated examples also show that the best approximate solutions of various problems are constructed for distinct values of parameter λ. Moreover, the efficiency and reliability of this technique are verified by the numerical examples.

Suggested Citation

  • Mine Aylin Bayrak & Ali Demir & Ebru Ozbilge, 2022. "An Improved Version of Residual Power Series Method for Space‐Time Fractional Problems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:6174688
    DOI: 10.1155/2022/6174688
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    References listed on IDEAS

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    5. 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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