Abstract
This article concerns with the existence and uniqueness for a new model of implicit coupled system of neutral fractional differential equations involving Caputo fractional derivatives with respect to the Chebyshev norm. In addition, we prove the Hyers–Ulam–Mittag-Leffler stability for the considered system through the Picard operator. For application of the theory, we add an example at the end. The obtained results can be extended for the Bielecki norm.
Highlights
Models of fractional differential equations (FDEs) have many applications in various fields of engineering and science such as mechanics, electricity, biology, chemistry, physics, and control and signal processing[1, 2]
For the different materials and phenomena, the heredity characteristics are well explained by FDEs, and as a result, many research papers and books have been published in this field [3,4,5,6,7]
FDEs in which the highest fractional derivatives (FDs) of unknown term appear both with and without delays are known as neutral FDEs
Summary
Models of fractional differential equations (FDEs) have many applications in various fields of engineering and science such as mechanics, electricity, biology, chemistry, physics, and control and signal processing[1, 2]. Different attempts have been made for the investigation of solutions of fractional and neutral FDEs [9,10,11,12,13,14,15,16,17] Another imperative and more remarkable area of research is committed to the stability analysis of the solutions for the FDEs and ordinary orders. As far as we know, results on EU and HUML stability for a coupled system of neutral FDEs have not been investigated. Motivated by the abovementioned work, in this article, we study the EU and HUML stability of the following implicit coupled neutral FDEs system involving Caputo FDs. 2.
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