Dynamics and stability of complex-order fractional hybrid Pantograph equations

Abstract

In this work, we investigate the Hyers-Ulam stability and existence of solutions to a class of fractional hybrid pantograph equations of complex order. First, we define the Caputo fractional derivative and show how it can be extended to complex orders. Next, we apply Dhage's Fixed Point Theorem to prove the existence of solutions. Lastly, we show Hyers-Ulam (H-U) stability, which means that modest changes in the governing equation only cause slight variations in the solutions. With possible uses in a number of scientific and engineering domains, this work expands our knowledge of stability in complex-order fractional differential equations.