Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with Fins

Abstract

The development in the qualitative theory of fractional differential equations is accompanied by discrete analog which has been studied intensively in recent past. Suitable fixed point theorem is to be selected to study the boundary value discrete fractional equations due to the properties exhibited by fractional difference operators. This article aims at investigating the stability results in the sense of Hyers and Ulam with application of Mittag–Leffler function hybrid fractional order difference equation of second type. The symmetric structure of the operators defined in this article is vital in establishing the existence results by using Krasnoselkii’s fixed point theorem. Banach contraction mapping principle and Krasnoselkii’s fixed point theorem are employed to establish the uniqueness and existence results for solution of fractional order discrete equation. A problem on heat transfer with fins is provided as an application to considered hybrid type fractional order difference equation and the stability results are demonstrated with simulations.

Keywords

• fractional order
• discrete
• Mittag–Leffler function
• boundary value problems
• Hyers Ulam stability