A NOVEL FRACTIONAL OPERATOR APPROACH TO CAUCHY-TYPE PROBLEMS: EXISTENCE, UNIQUENESS, AND STABILITY

Abstract

This research employs an innovative methodology to investigate the existence, uniqueness, and stability of solutions to a Cauchy-type problem with a fractional variable order. In contrast to the methodologies employed in existing literature, which primarily focus on the utilization of generalized intervals and the concept of piecewise constant functions, we propose a novel fractional operator that is more suitable for the task at hand. Furthermore, we provide evidence of the solvability and stability of the primary problem. The efficacy of our technique is derived from its simplicity and reliance on fewer limiting assumptions. The document is concluded by the inclusion of an application, which encompasses an illustrative example along with accompanying visual aids.