Conditions to guarantee the existence of solutions for a nonlinear and implicit integro‐differential equation with variable coefficients

Source abstract

Using Babenko's approach, multivariate Mittag–Leffler (MM–L) function, and Krasnoselskii's fixed point theorem, we first investigate the existence of solutions to a Liouville–Caputo nonlinear integro‐differential equation with variable coefficients and initial conditions in a Banach space. Then the existence of a positive solution for a variant equation is studied. Finally, we provide examples to illustrate the applications of the main results obtained.