New Approach for Analysis of Solution of Certain Fractional Sum-Difference Equations

Abstract

This paper investigates a class of nonlinear fractional sum–difference equations in a discrete setting. By converting the considered problem into an equivalent fractional summation equation, fixed point techniques are effectively applied to analyze the behavior of solutions. The existence of solutions is established through the Leray–Schauder alternative, whereas uniqueness is derived using a discrete form of Bihari’s inequality. The obtained results extend several existing works related to fractional discrete systems under suitable growth conditions. Moreover, the developed approach offers an efficient framework for studying nonlinear fractional dynamical models with memory effects arising in discrete fractional calculus.