NEW GENERALIZATION INVOLVING CONVEX FUNCTIONS VIA ℏ-DISCRETE 𝒜ℬ-FRACTIONAL SUMS AND THEIR APPLICATIONS IN FRACTIONAL DIFFERENCE EQUATIONS

Abstract

The purpose of this paper is to explore novel variants for convex functions via discrete [Formula: see text]-fractional operator in the frame of time scale calculus [Formula: see text] with [Formula: see text] and [Formula: see text] Based on a comparison with the integral inequalities, we have provided new discrete fractional inequalities having [Formula: see text]-discrete generalized Mittag-Leffler function in the kernel which generates several known results and can be utilized as handy tools in the investigation of qualitative and quantitative properties of solutions of certain classes of difference equations. Several new special cases are also apprehended in the setting of time scale [Formula: see text] and [Formula: see text] As the application aspect, we provide an illustrated example to show the effectiveness of our new criteria in fractional [Formula: see text]-difference type initial value problem.