Differential equations in classical sequence spaces

Abstract

Measures of noncompactness are very useful tools which are widely used in fixed point theory, differential equations, functional equations, integral and integro-differential equations, and optimization etc. In recent years measures of noncompactness have also been used in defining geometric properties of Banach spaces as well as in characterizing compact operators between sequence spaces. In this survey article, we present a study on applications of measures of noncompactness to infinite system of differential equations of first and second order and fractional differential equations in some classical sequence spaces.