A NOVEL FIXED POINT ITERATION PROCEDURE FOR APPROXIMATING THE SOLUTION OF IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

In this research, we propose a new efficient iterative method for fixed point problemsof generalized α-nonexpansive mappings. We show the weak and strong convergence analysis of the proposed method under some mild assumptions on the control parameters.We consider the application of the new method to some real world problems such as convex minimization problems, image restoration problems and impulsive fractional differential equations. We carryout a numerical experiment to show the computational advantage of ourmethod over some well known existing methods.