Generalization of Darbo-type theorem and application on existence of implicit fractional integral equations in tempered sequence spaces

Abstract

The aim of this work is to give some fixed point results based on the technique of measure of noncompactness which extend the classical Darbo’s theorem. With the help of our Darbo-type theorem, we obtain the existence of solution of implicit fractional integral equations in C(I,ℓpα) (collection of all continuous functions from I=[0,a] (a>0) to ℓpα), where ℓpα is a tempered sequence space. Finally, we present a numerical example to see the validity and practicability of our existence result.

Keywords

• 45G15
• 46B45
• 47H08
• 47H10