Existence result for nonlinear pantograph fractional differential equations involving generalized Caputo derivative

In this paper, we are interested in proving the existence, uniqueness and stability of solutions to nonlinear pantograph fractional differential equations involving the generalized Caputo derivative with nonlocal conditions. To obtain the main results, we examine two classical theorems of functional analysis, the Schaefer fixed point theorem and the Banach contraction principle. Furthermore, we explore the stability of the solutions by analogy with the Ulam-Hyers theory. Finally, as applications of the theoretical results, we provide specific examples to demonstrate the practicality and validity of the key findings.