A Measure of Noncompactness Method for Nonlinear Conformable Pantograph Differential Equations

Abstract

This work is devoted to the study of existence results for a class of nonlinear conformable fractional pantograph differential equations subject to nonlocal initial conditions. By employing the conformable fractional derivative of order β∈(1,2), the considered problem is transformed into an equivalent integral equation. The Kuratowski measure of noncompactness combined with topological degree theory for condensing operators is then used to establish the existence and boundedness of solutions. An illustrative example is presented to highlight the applicability of the theoretical findings.