On the solvability and approximate solution of a one-dimensional singular problem for a p-Laplacian fractional differential equation

KumSong Jong, HuiChol Choi, MunChol Kim, KwangHyok Kim, SinHyok Jo and Ok Ri

Chaos, Solitons & Fractals, 2021, vol. 147, issue C

Abstract: In this paper, using the monotone iterative technique, we discuss a new approximate method for solving multi-point boundary value problems of p-Laplacian fractional differential equations with singularities, which are of great importance in the fluid dynamics field. To do this, first, a sequence of auxiliary problems that release the nonlinear source terms contained in the equations from the singularities is set up, and the uniqueness and existence of their positive solutions are established. Next, we show the relative compactness of the sequence of unique solutions to these auxiliary problems to prove the solvability of our given problem. And we present some sufficient conditions to construct a sequence of approximate solutions that converges to an exact solution of our problem. Finally, we give two numerical examples to demonstrate our main results.

Keywords: Fractional differential equation; p-Laplacian operator; Singular source term; Muti-point boundary value problem; Turbulent flow in porous medium (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003027

DOI: 10.1016/j.chaos.2021.110948

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