Solvability of a System of Nonlinear Integral Equations with a General Kernel

Abstract

This study establishes the adequate conditions for the solvability of a Volterra-type nonlinear system of integral equations with some general kernels. The proof of the existence result is established in the space C (I; B 1 B 2), where B 1 and B 2 represent two arbitrary Banach spaces. Darbo’s fixed point theorem and the methodologies for noncompactness measures are employed in our analysis. Moreover, we study the Cauchy problem for a system of fractional di¤erential equations. Finally, we present some examples in sequence spaces that demonstrate the application of our results to specific kernels and a class of more general kernels that satisfy a specific condition. Mathematics Subject Classification: 47H08, 47G15, 47H10.