Method of a Priori Estimate in the Case of Fractional Order Differential Equations with Integral Conditions

Abstract

This paper concentrate on exploring the existence and uniqueness of a solution for a non-linear boundary value problem that has integral conditions in the case of fractional partial differential equations. For this we split the proof into two sections: linear and non-linear problem; for the associated linear problem, we derive the a priori bound and demonstrate the density of the operator generated by the problem posed; we solve the non-linear problem by introducing a iterative process. The results show the efficiency of energy inequality method in the case of time fractional order differential equations with integral conditions our results illustrate the existence and uniqueness of the continuous dependence of solution on fractional order.