Existence of a solution of Hilfer fractional hybrid problems via new Krasnoselskii-type fixed point theorems

Abstract

This work intends to treat the existence of mild solutions for the Hilfer fractional hybrid differential equation (HFHDE) with linear perturbation of first and second type in partially ordered Banach spaces. First, we establish the results concerning the actuality of fixed point of sum and product of operators via the concepts of measure of noncompactness and simulation functions in partially ordered spaces. Then combining these fixed point theorems with the concepts in fractional calculus, new existence results for mild solutions of HFHDE’s are established. Furthermore, the presented fixed point results and existence results improve and extend the present state-of-art in the literature. Competent examples in support of theory are illustrated for better understanding.

Keywords

• partially ordered spaces (algebra)
• coupled fixed point
• measure of noncompactness
• hilfer fractional derivative
• fractional hybrid differential equation
• 47h10
• 34a08
• 34k37
• 47h08