Monotone Iterative Technique for Systems of Nonlinear Fractional Differential Equations on Time Scales

Abstract

Fractional differential equations play an important role in describing many phenomena and processes in various elds of science such as physics, chemistry, control systems, population dynamics, aerodynamics and electrodynamics, etc. In this work, we present existence of quasi-solutions for the rs-order dynamic equations involving integral boundary conditions, and we present the existence of extremal solutions for nonlinear conformable fractional di erential equations involving integral boundary conditions. Also, we present the existence of extremal solutions for a coupled system of nonlinear conformable fractional di erential equations on time scales with initial conditions. Existence results for these problems are obtained by by applying the comparison principle and the monotone iterative technique combined with the method of upper and lower solutions.