Existence and Stability Results for Fractional Fully Hybrid Elastic Beam Equation: Caputo‐Like Formulation

ABSTRACT In this article, a fully hybrid elastic beam equation (EBE) is characterized by a fractional difference equation of the fourth‐order involving the Caputo‐like fractional difference operator. In this direction, the existence of the unique solution for the system is discussed in the context of fixed‐point theorems. Next, several kinds of stability properties are investigated. Finally, numerical examples, graphic representations, and numerical tables are given to illustrate the performance of both Caputo‐like difference operators by varying various parameters in the proposed mathematical model.