Existence results for infinite systems of the Hilfer fractional boundary value problems in Banach sequence spaces

Abstract

Abstract The main aim of this paper is to present some existence criteria for an infinite system of Hilfer fractional boundary value problems of the form D a + α , β u i = − F i ( t , u ) , u i ( a ) = u i ( b ) = 0 , a < t < b , i = 1 , 2 , … , $$ \mathcal{D}_{a^{+}}^{\alpha,\beta }u_{i}=-F_{i}(t,u),\quad u_{i}(a)=u_{i}(b)=0, a< t< b,i=1,2,\ldots, $$ in Banach sequence spaces of c 0 $c_{0}$ and l p , p ≥ 1 $l_{p},p\geq 1$ types. Our approach is based on the Darbo-type fixed point theorems acting on the condensing operators. The obtained existence results in each of the above sequence spaces are illustrated by presenting some numerical examples.

Keywords

• Infinite systems of fractional differential equations
• Hilfer fractional derivatives
• Measure on noncompactness
• Condensing operators
• Darbo-type fixed point theorem
• Existence of solutions