Existence and Uniqueness of Solutions for Caputo Fractional High-Order Multi-Point Boundary Value Problems with Applications

Abdolrazaghi, Fatemeh

doi:10.311581/JAMDA.2509.1016.1.2.6

Existence and Uniqueness of Solutions for Caputo Fractional High-Order Multi-Point Boundary Value Problems with Applications

Document Type : Research Article

Author

Fatemeh Abdolrazaghi

Imam Khomeini International University

10.311581/JAMDA.2509.1016.1.2.6

Abstract

This research paper addresses the existence and uniqueness of solutions for a class of high-order nonlinear boundary value problems involving the Caputo fractional derivative and non-local multi-point boundary conditions. Our analytical approach primarily relies on constructing a novel fractional Green’s function for the problem. Subsequently, we apply the Banach contraction principle to establish the existence and uniqueness of solutions. To demonstrate the applicability and validity of our theoretical results, we provide a detailed illustrative example. This work contributes to the understanding of complex fractional differential equations, which are essential in modeling various phenomena across science and engineering.

Keywords

High-order fractional differential equation

Caputo fractional derivative

Boundary value problem

Existence and uniqueness

Fixed point theorem