Inhomogeneous generalized fractional Bessel differential equations in complex domain

Abstract

This paper explores inhomogeneous generalized fractional-order Bessel differential equations in the complex domain with arbitrary-order δ () using Riemann-Liouville (R-L) fractional operators. The study establishes the existence of holomorphic solutions through the power series method, considering the concept of radius of convergence. Conditions for the unique existence of holomorphic solutions in the complex domain are identified using fixed point theory and the Rouche theorem. Additionally, the paper demonstrates that the solution, particularly for infinite series of fractional power, satisfies the generalized Ulam-Hyers stability. Furthermore, when , the solution to the inhomogeneous Bessel differential equation takes the form of Bessel functions of the first kind, denoted as .