<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This paper deals with a new class of mixed fractional differential equations with integral boundary conditions. We show an important equivalence result between our problem and nonlinear integral Fredholm equation of the second kind. The existence and uniqueness of a positive solution are proved using Guo-Krasnoselskii’s fixed point theorem and Banach’s contraction mapping principle. Different types of Ulam-Hyers stability are discussed. Three examples are also given to show the applicability of our results.</p>
</abstract>

This paper deals with a new class of mixed fractional differential equations with integral boundary conditions. We show an important equivalence result between our problem and nonlinear integral Fredholm equation of the second kind. The existence and uniqueness of a positive solution are proved using Guo-Krasnoselskii’s fixed point theorem and Banach’s contraction mapping principle. Different types of Ulam-Hyers stability are discussed. Three examples are also given to show the applicability of our results.

A new class of mixed fractional differential equations with integral boundary conditions

Laboratory of Pure and Applied Mathematics

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This paper deals with a new class of mixed fractional differential equations with integral boundary conditions. We show an important equivalence result between...

A new class of mixed fractional differential equations with integral boundary conditions

Published Online: Dec 28, 2020

Page range: 227 - 247

Received: Aug 31, 2020

Accepted: Dec 05, 2020

DOI: https://doi.org/10.2478/mjpaa-2021-0016

Keywords
Caputo fractional derivative, Conformable fractional derivative, Fixed point theorems, Positive solution, Ulam-Hyers stability

© 2020 Djiab Somia et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A new class of mixed fractional differential equations with integral boundary conditions

Published Online: Dec 28, 2020

Page range: 227 - 247

Received: Aug 31, 2020

Accepted: Dec 05, 2020

DOI: https://doi.org/10.2478/mjpaa-2021-0016

KeywordsCaputo fractional derivative, Conformable fractional derivative, Fixed point theorems, Positive solution, Ulam-Hyers stability

© 2020 Djiab Somia et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Caputo fractional derivative, Conformable fractional derivative, Fixed point theorems, Positive solution, Ulam-Hyers stability