Existence and non-existence results for higher order fractional boundary value problem

Barbara Łupińska

doi:10.3934/dcdsb.2025081

Article Contents

2025, Volume 30, Issue 11: 4383-4393. Doi: 10.3934/dcdsb.2025081

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Existence and non-existence results for higher order fractional boundary value problem

Barbara Łupińska

Faculty of Computer Science, University of Bialystok, Poland

Received: October 2024

Revised: May 2025

Early access: May 22, 2025

Published online: May 22, 2025

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Abstract

In this paper, we discuss the existence and the uniqueness of solutions for a class of nonlinear fractional differential equations with a mixed fractional boundary value by using Banach fixed point theorem. Moreover, we compare the obtained results with another two works considering similar problem.

Keywords:

Non-linear fractional differential equations,
fix point theorem,
Katugampola fractional derivative,
mixed boundary value problem.

Mathematics Subject Classification: Primary: 26A33, 34A08; Secondary: 35A23.

Citation:

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Figure 1. The partial estimation of $ \lambda $ for $ \alpha = 1.5,\ \alpha = 1.1 $, and $ \alpha = \frac{13}{7} $

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