The study of a separated boundary value problem for a fractional equation involving a derivative of lower order at the Schauder fixed point

Authors

  • Djebaili Manel, Merad Ahcene

Keywords:

fractional differential equation, separated fractional boundary conditions, Schauder fixed point theorem, existence.

Abstract

In this study, we explore a new category of separated boundary value problems for non-linear fractional differential equations where the non-linear term f relies on a lower-order fractional derivative given by:

subject to separated fractional boundary conditions :

,

Here,  is the Caputo fractional derivative, f: [0,T] ×→is a continuous function, and , ,  ,i = 1, 2 are real constants satisfying:   0 and T > 0.

The aim of this work is to study the existence and uniqueness of solutions to the separated fractional boundary value problem using the Schauder fixed point theorem, which is a topological theorem that asserts a relatively compact map has a fixed point that is not necessarily unique. Therefore, it is not necessary to establish estimates on the function, but rather on its compactness.

To conclude, an example is presented to illustrate the application of this theorem.

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Published

2024-02-21

How to Cite

Djebaili Manel, Merad Ahcene. (2024). The study of a separated boundary value problem for a fractional equation involving a derivative of lower order at the Schauder fixed point. Utilitas Mathematica, 120, 1191–1199. Retrieved from https://utilitasmathematica.com/index.php/Index/article/view/1874

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