Logarithmic Chelyshkov functions for one- and two-dimensional nonlinear Caputo–Hadamard fractional Rosenau equation

M.H. Heydari, M. Hosseininia and M. Razzaghi

Chaos, Solitons & Fractals, 2024, vol. 185, issue C

Abstract: In this work, the Caputo–Hadamard time fractional version of the Rosenau equation in one and two dimensions is introduced. The logarithmic Chelyshkov functions (LCFs), as a novel family of basis functions, are introduced and used together with the classical Chelyshkov polynomials (CCPs) to established a hybrid method to solve the expressed fractional equations. For this aim, the ordinary and fractional derivative matrices associated with these basis functions are determined. To establish the desired approach by considering a hybrid expansion of the fractional problem’s solution using the CCPs (for the spatial variables) and LCFs (for the temporal variable), and employing the derived derivative matrices, solving the fractional problem under consideration turns into solving an algebraic system of nonlinear equations. Some numerical examples are considered to investigate the capability and accuracy of this proposed scheme.

Keywords: Chelyshkov polynomials; Logarithmic Chelyshkov functions; Caputo–Hadamard fractional derivative; Rosenau equation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924007380

DOI: 10.1016/j.chaos.2024.115186

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