Some new uniqueness and Ulam stability results for a class of Multi-Terms fractional differential equations in the framework of Generalized Caputo Fractional Derivative using the $\Phi$-fractional Bielecki-type norm

Authors

CHOUKRI DERBAZI
ZIDANE BAITICHE
MICHAL FECKAN

Abstract

In this research article, a novel $\Phi$-fractional Bielecki-type norm introduced by Sousa and Oliveira [23] is used to obtain results on uniqueness and Ulam stability of solutions for a new class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative. The uniqueness results are obtained by employing Banach' and Perov's fixed point theorems. While the $\Phi$-fractional Gronwall type inequality and the concept of the matrices converging to zero are implemented to examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, two illustrative examples are provided to demonstrate the validity of our theoretical findings.

DOI

10.3906/mat-2011-92

Keywords

$\Phi $-Caputo fractional derivative, fixed point, uniqueness, $\Phi$-fractional Bielecki-type norm, $\mathbb E_{\mu}$-Ulam stability

First Page

2307

Last Page

2322

Recommended Citation

DERBAZI, C, BAITICHE, Z, & FECKAN, M (2021). Some new uniqueness and Ulam stability results for a class of Multi-Terms fractional differential equations in the framework of Generalized Caputo Fractional Derivative using the $\Phi$-fractional Bielecki-type norm. Turkish Journal of Mathematics 45 (5): 2307-2322. https://doi.org/10.3906/mat-2011-92