Existence results for weakly coupled system of ψ-Caputo fractional differential equations with nonlinear boundary conditions

Abstract

unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract. In this paper, our aim is to develop monotone iterative technique by introducing the notion of coupled upper, lower and quasi solutions and apply it to prove existence of solution of nonlinear boundary value problems for weakly coupled system of ψ-Caputo fractional differential equations. We choose suitable initial iterations and construct two monotone sequences which converge monotonically from above and below to quasi solutions of nonlinear weakly coupled system of ψ-Caputo fractional differential equations. Further we show that these sequences lead to existence of solution of nonlinear boundary value problem for weakly coupled system of ψCaputo fractional differential equations.