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CMMSE: Existence and Uniqueness of Positive Solution for Fractional Differential Equation involving ρ(τ)-Laplacian Operator and Nonlocal Integral Condition
  • Piyachat Borisut,
  • Supak Phiangsungnoen
Piyachat Borisut
Rajamangala University of Technology Rattanakosin - Bophit Phimuk Chakkrawat Campus
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Supak Phiangsungnoen
Rajamangala University of Technology Rattanakosin - Bophit Phimuk Chakkrawat Campus

Corresponding Author:[email protected]

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Abstract

This paper aims to investigate the Caputo fractional differential equation involving ρ(τ) Laplacian operator and nonlocal multi-point of Riemann-Lioville’s fractional integral. We also prove the uniqueness of positive solutions for Boyd and Wong’s non-linear contraction via the Guo-Krasnoselskii fixed point theorems in Banach spaces. Finally, we illustrate the theoretical results and show that by solving the nonlocal problems is possible to obtain accurate approximations of the solutions.