Hyers-Ulam stability of fractional hybrid differential equation in Hölder space

Abstract

The current paper’s goal is to study about solvability of the fractional hybrid differential equation in tempered space. Also, the uniqueness and the stability of the solution are examined. In order to demonstrate the Hyers-Ulam stability of the aforementioned differential equation, we employ the fixed-point approach. The results reported in the study are situated inside the domain of tempered and continuous functions on the closed interval [Formula: see text]. The key tools in this case are the Schauder’s FPT and Banach FPT. The advantage of this space is having a suitable conjunction with Schauder’s FPT. Schauder’s FPT is quite handy for the space whose growths are tempered by modulus of continuity. Compactness is one of the requirement of Schauder’s FPT but if we consider any bounded subset in those spaces, it is relatively compact as well as compact. We present an example to demonstrate how our findings can be applied.

Keywords

• Hyers-Ulam stability
• fractional hybrid differential equation
• Holder space
• fixed-point approach
• Schauder and the Darbo fixed-point theorems
• 26B35