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Adaptation on power series method with conformable operator for solving fractional order systems of nonlinear partial differential equations

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  • Liaqat, Muhammad Imran
  • Khan, Adnan
  • Akgül, Ali

Abstract

The aim of this research work is to modify the power series solution method to fractional order in the sense of conformable derivative to solve a coupled system of nonlinear fractional partial differential equations. We called it the conformable fractional power series method. To evaluate its efficiency and consistency, absolute errors of three problems are considered numerically. Consequences established that our recommended method is unpretentious, accurate, valid, and capable. When solving the nonlinear complications, it has a powerful superiority over the homotopy analysis and Adomian decomposition methods. Additional as in the residual power series method through generating the coefficients for a series, it is compulsory to calculate the fractional derivatives on every occasion, whereas this method only needs the idea of equating coefficients. The convergence and error analyses of the series solutions are also presented.

Suggested Citation

  • Liaqat, Muhammad Imran & Khan, Adnan & Akgül, Ali, 2022. "Adaptation on power series method with conformable operator for solving fractional order systems of nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
  • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001941
    DOI: 10.1016/j.chaos.2022.111984
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    References listed on IDEAS

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    1. Adnan Khan & Muhammad Imran Liaqat & Muhammad Younis & Ashraful Alam & Fairouz Tchier, 2021. "Approximate and Exact Solutions to Fractional Order Cauchy Reaction-Diffusion Equations by New Combine Techniques," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, December.
    2. Rasool Shah & Hassan Khan & Poom Kumam & Muhammad Arif & Dumitru Baleanu, 2019. "Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay," Mathematics, MDPI, vol. 7(6), pages 1-14, June.
    3. Bashir Ahmad & Jorge Losada & Juan J. Nieto, 2015. "On Antiperiodic Nonlocal Three-Point Boundary Value Problems for Nonlinear Fractional Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-7, June.
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    5. Haidong Qu & Zihang She & Xuan Liu, 2020. "Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations," Complexity, Hindawi, vol. 2020, pages 1-13, July.
    6. E. López-Sandoval & A. Mello & J. J. Godina-Nava & A. R. Samana, 2015. "Power Series Solution for Solving Nonlinear Burgers-Type Equations," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-9, October.
    7. Hasan, Shatha & Al-Smadi, Mohammed & El-Ajou, Ahmad & Momani, Shaher & Hadid, Samir & Al-Zhour, Zeyad, 2021. "Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    8. Balcı, Ercan & Öztürk, İlhan & Kartal, Senol, 2019. "Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 43-51.
    9. Qinwu Xu & Zhoushun Zheng, 2019. "Spectral Collocation Method for Fractional Differential/Integral Equations with Generalized Fractional Operator," International Journal of Differential Equations, Hindawi, vol. 2019, pages 1-14, January.
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    Cited by:

    1. 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.
    2. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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