Journal
Turkish Journal of Science
Volume & Issue
Volume 9, Issue 3
Published on
November 26, 2024
Pages
174-180
DOI
Article
A Work on Cauchy Problems for Variable-Order Derivatives with Exponential Kernel
Authors
Ilknur KOCA
Abstract
In this work, we study the existence and uniqueness of solutions to variable-order fractional differential equations with exponential kernel. The Caputo-Fabrizio definition is used for the variable-order fractional derivative with the order being a bounded function. To prove the existence of solutions for the Cauchy problem, we develop an iterative sequence. Finally, uniqueness is verified via linear growth and Lipschitz conditions.