A solution of the fractional differential equations in the setting of b-metric space

In this paper, we study the existence of solutions for the following differential equations by using a fixed point theorems \[ {cases} Dμcw()± Dνcw()=h(,w()),& ∈ J,\ \ 0<ν<μ<1,\\ w(0)=w_0,& \ {cases} \] where Dμ, Dν is the Caputo derivative of order μ, ν, respectively and h:J× R→ R is continuous. The results are well demonstrated with the aid of exciting examples.