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

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 $$ \mathcal{D}_{a^{+}}^{\alpha,\beta }u_{i}=-F_{i}(t,u),\quad u_{i}(a)=u_{i}(b)=0, a< t< b,i=1,2,\ldots, $$ D a + α , β u i = − F i ( t , u ) , u i ( a ) = u i ( b ) = 0 , a < t < b , i = 1 , 2 , … , in Banach sequence spaces of $c_{0}$ c 0 and $l_{p},p\geq 1$ l p , p ≥ 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.