DineshVerma transform and ulam type stability of fractional differential equations

This thesis addresses the Hyers-Ulam type stability of fractional linear differential equations via a novel integral operator known as the Dinesh Verma transform. The thesis is structured into five chapters. The first chapter provides a historical overview of the concept of fractional derivatives, along with introductory information on the Caputo fractional derivative, the Dinesh Verma transform, and Hyers-Ulam stability. In the second chapter, titled Materials and Methods, the fundamental definitions and theorems used throughout the thesis are presented, followed by the definitions and properties of the Caputo fractional derivative and the Dinesh Verma transform. In the third chapter, the historical background of Hyers-Ulam stability is presented first. Subsequently, Dinesh Verma transformations of certain functions were derived, and the Hyers-Ulam type stability of linear fractional differential equations involving the Caputo fractional derivative was investigated. The fourth chapter is devoted to discussion. Finally, the fifth chapter summarizes the main findings of the study and offers several suggestions for future research.