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

Hang Xu

Chaos, Solitons & Fractals, 2023, vol. 166, issue C

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.

Keywords: Fractional differential equation; Analytical approximation; Arbitrary accuracy; Scaling transformation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010967

DOI: 10.1016/j.chaos.2022.112917

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