An Implicit Fractional Model With Finite Delay and Impulses: Analysis and Computation

This paper establishes the existence and uniqueness of solutions for a class of implicit fractional Volterra–Fredholm integrodifferential equations with finite delay and instantaneous impulses. By employing the Banach contraction principle and Schaefer’s fixed-point theorem, we provide a rigorous analytical foundation for our results. Furthermore, through illustrative examples and numerical simulations, we validate our theoretical findings, which provide a deeper understanding of the problem’s behavior for researchers. Our work not only advances the theoretical framework of impulsive fractional dynamic systems but also provides practical tools for further exploration in applied mathematics and related fields.