On Hybrid and Non-Hybrid Discrete Fractional Difference Inclusion Problems for the Elastic Beam Equation

Abstract

The results in this paper are related to the existence of solutions to hybrid and non-hybrid discrete fractional three-point boundary value inclusion problems for the elastic beam equation. The development of our results is attributed to the use of the Caputo and difference operators. The existence results for the non-hybrid discrete fractional inclusion problem are established by using fixed point theory for multi-valued upper semi-continuous maps, and the case of the hybrid discrete fractional inclusion problem is treated by Dhage’s fixed point theory. Additionally, we present two examples to illustrate our main results.

Keywords

• hybrid elastic beam equation
• fractional difference equation
• fixed point theorems
• existence
• stability analysis
• iterative methods