Nonlinear fractional differential equations with advanced arguments

Document Type : Research Paper


1 Department of Mathematics, Faculty of Education, Applied Sciences and Arts, Amran University, Amran, Yemen

2 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad - 431004, India


In this paper, we develop the existence and uniqueness theory of fractional differential equation involving Riemann-Liouville differential operator of order $0 < \alpha< 1$, with advanced argument and integral boundary conditions. We investigate the uniqueness of the solution by using Banach fixed point theorem, we apply the comparison result to obtain the existence and uniqueness of solution by monotone iterative technique also by using weakly coupled extremal solution for the nonlinear boundary value problem (BVP). As an application of this technique, existence and uniqueness results are obtained.