Work

Existence and stability analysis of a problem of the Caputo fractional derivative with mixed conditions

Year: 2025

Type: article

Abstract: Recently, initial-boundary-value problems with the Caputo fractional derivative for ordinary differential equations have been intensively studied. This paper studies a nonlinear integro-differential equation of fractional order, containing a composition of fractional derivatives with different origins and mixed conditions. The equation under consideration acts as a model equation of motion in a fractal medium. First, we use three fixed-point theorems to prove the existence and uniqueness results. Then, the Ulam stability criterion of the solution is given. The main results will be illustrated by a proposed example.

Source: AIMS Mathematics

DOI: 10.3934/math.2025312

Authors: Naimi Abdellouahab, Keltum Bouhali, Loay Alkhalifa, Khaled Zennir

Institutions: University of Ghardaia, Qassim University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: Qassim University