Ulam-Hyers Stability of Ψ-Hilfer Volterra Integro-Differential Equations of Fractional Order Containing Multiple Variable Delays

Abstract

The authors consider a nonlinear psi-Hilfer fractional-order Volterra integro-differential equation (psi-Hilfer FrOVIDE) that incorporates N-multiple variable time delays into the equation. By utilizing the psi-Hilfer fractional derivative, they investigate the Ulam-Hyers-Rassias and Ulam-Hyers stability of the equation by using fixed-point methods. Their results improve existing ones both with and without delays by extending them to nonlinear psi-Hilfer FrOVIDEs that incorporate N-multiple variable time delays.