On Existence and Uniqueness of Solutions to a Class of Fractional Volterra-Fredholm Initial Value Problems - Sharif, Abdulrahman A.; Hamoud, Ahmed A.; Ghadle, Kirtiwant P. (Discontinuity, Nonlinearity, and Complexity, 2026)
In this paper, we establish some new conditions for the existence of solutions for a class of nonlinear Caputo fractional Volterra-Fredholm integro-differential equations with initial conditions. The desired results are proved by using Banach fixed point theorem for nonself mappings, fractional inequality and a version of the nonlinear alternative of Leray-Schauder in Banach spaces. Furthermore, the uniqueness results are established by the application of the contraction mapping principle. Finally, some examples are proposed to illustrate our main results.