A Nonlinear Fractional Problem with Mixed Volterra-Fredholm Integro-Differential Equation: Existence, Uniqueness, H-U-R Stability, and Regularity of Solutions

Abstract

This paper considers nonlinear fractional mixed Volterra-Fredholm integro-differential equation with a nonlocal initial condition. We propose a fixed-point approach to investigate the existence, uniqueness, and Hyers-Ulam-Rassias stability of solutions. Results of this paper are based on nonstandard assumptions and hypothesis and provide a supplementary result concerning the regularity of solutions. We show and illustrate the wide validity field of our findings by an example of problem with nonlocal neutral pantograph equation, involving functional derivative and $\psi$ -Caputo fractional derivative.