Li, ChenkuanSaadati, RezaAllahviranloo, Tofigh2022-12-152022-12-152022Li, C., Saadati, R., & Allahviranloo, T. Conditions to guarantee the existence of solutions for a nonlinear and implicit integro‐differential equation with variable coefficients. Mathematical Methods in the Applied Sciences.0170-42141099-1476http://dx.doi.org/10.1002/mma.8890https://hdl.handle.net/20.500.12713/3482Using 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.eninfo:eu-repo/semantics/closedAccessBabenko's ApproachKrasnoselskii's Fixed Point TheoremMM-L FunctionArticleWOS:0008883517000012-s2.0-85142334551Q110.1002/mma.8890Q1