p-Laplacian Fractional Sturm-Liouville Problem for Diffusion Operator via Impulsive Condition

TL;DR

This paper investigates the existence of solutions for a fractional p-Laplacian Sturm-Liouville problem involving diffusion operators with impulsive conditions, using fixed point theory and fractional calculus.

Contribution

It introduces new existence results for fractional p-Laplacian problems with impulsive conditions, employing Riemann-Liouville and Caputo derivatives and Schaefer fixed point theorem.

Findings

Existence of solutions established for the problem.

Integral representation of solutions derived.

Application of Schaefer fixed point theorem confirmed solutions' existence.

Abstract

In this study, the existence results of solution is given for fractional p-Laplacian Stum-Liouville problem for diffusion operator of order with impulsive conditions. The derivatives are described in Riemann-Liouville and Caputo sense. The Riemann-Liouville integral operator is used to acquire the integral representation of solution. The existence of solution is demonstrate via Schaefer fixed point theorem.