Existence and κ-Mittag-Leffler-Ulam-Hyers stability results for implicit coupled (κ,ϑ)-fractional differential systems

Abstract

AbstractIn this paper, we delve into the analysis of the existence and stability concerning the [Formula: see text]-Mittag-Leffler-Ulam-Hyers within a particular class of coupled systems related to boundary value problems. These problems entail implicit nonlinear fractional differential equations and [Formula: see text]-generalized ϑ-Hilfer fractional derivatives. To achieve our objectives, we employ the Mönch fixed point theorem, complemented by the application of the measure of noncompactness technique and an extension of the well-established Gronwall inequality. Furthermore, we include an illustrative example to showcase the practical utility of our results. The significance of our research lies in examining a comprehensive problem involving coupled systems, which serves as a generalization encompassing all the works mentioned in the introduction. It is viewed as a logical extension and continuation within the framework of this continually evolving theory.

Keywords

• Banach spaces
• coupled systems
• existence
• generalized Gronwall inequality
• generalized Hilfer fractional derivative
• measure of noncompactness