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

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

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.

Suggested Citation

  • Jong, KumSong & Choi, HuiChol & Kim, MunChol & Kim, KwangHyok & Jo, SinHyok & Ri, Ok, 2021. "On the solvability and approximate solution of a one-dimensional singular problem for a p-Laplacian fractional differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003027
    DOI: 10.1016/j.chaos.2021.110948
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    References listed on IDEAS

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    1. Wang, Fang & Liu, Lishan & Wu, Yonghong, 2020. "A numerical algorithm for a class of fractional BVPs with p-Laplacian operator and singularity-the convergence and dependence analysis," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Fang Wang & Lishan Liu & Yonghong Wu & Yumei Zou, 2019. "Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p -Laplacian Operator," Complexity, Hindawi, vol. 2019, pages 1-21, October.
    3. Škovránek, Tomáš & Podlubny, Igor & Petráš, Ivo, 2012. "Modeling of the national economies in state-space: A fractional calculus approach," Economic Modelling, Elsevier, vol. 29(4), pages 1322-1327.
    4. Abdulhameed, M. & Vieru, D. & Roslan, R., 2017. "Modeling electro-magneto-hydrodynamic thermo-fluidic transport of biofluids with new trend of fractional derivative without singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 233-252.
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