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A generalized analytical approach for highly accurate solutions of fractional differential equations

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  • Xu, Hang

Abstract

A generalized homotopy-based approach is developed to give highly accurate solutions of fractional differential equations. By introducing a scaling transformation, the computational domain of the nonlinear Riccati differential equations with fractional order changes from [0,+∞) to [0,1]. Analytical approximation of arbitrary accuracy is achieved, whose convergence is proved theoretically. The effectiveness and accuracy of our solution is strictly checked via error analysis. The proposed method is expected to be as a new and reliable analytical approach to give highly accurate solutions of strongly nonlinear problems in fractional calculus.

Suggested Citation

  • Xu, Hang, 2023. "A generalized analytical approach for highly accurate solutions of fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010967
    DOI: 10.1016/j.chaos.2022.112917
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    References listed on IDEAS

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    1. Cang, Jie & Tan, Yue & Xu, Hang & Liao, Shi-Jun, 2009. "Series solutions of non-linear Riccati differential equations with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 1-9.
    2. Fuzhang Wang & Muhammad Nawaz Khan & Imtiaz Ahmad & Hijaz Ahmad & Hanaa Abu-Zinadah & Yu-Ming Chu, 2022. "Numerical Solution Of Traveling Waves In Chemical Kinetics: Time-Fractional Fishers Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(02), pages 1-11, March.
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    4. Hijaz Ahmad & Tufail A. Khan & Predrag S. Stanimirović & Yu-Ming Chu & Imtiaz Ahmad, 2020. "Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models," Complexity, Hindawi, vol. 2020, pages 1-14, October.
    5. Jianxin Cao & Haibo Chen, 2011. "Positive Solution of Singular Fractional Differential Equation in Banach Space," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-22, November.
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    7. Hijaz Ahmad & Ali Akgül & Tufail A. Khan & Predrag S. Stanimirović & Yu-Ming Chu, 2020. "New Perspective on the Conventional Solutions of the Nonlinear Time-Fractional Partial Differential Equations," Complexity, Hindawi, vol. 2020, pages 1-10, October.
    8. Chu, Yu-Ming & Ullah, Saif & Ali, Muzaher & Tuzzahrah, Ghulam Fatima & Munir, Taj, 2022. "Numerical Investigation of Volterra Integral Equations of Second Kind using Optimal Homotopy Asymptotic Method," Applied Mathematics and Computation, Elsevier, vol. 430(C).
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