an existence result for some fractional-integro differential equations in banach spaces via deformable derivative

In this paper we investigate further properties of the deformable derivative and use the results to study the existence of solutions to the integro-differential equation d α y(t) = h(y(t)) + f(t, y(t)) + r t 0 k(t, s, y(s))ds, t ∈ [0, t], with initial condition y(0) = y0, where d α y(t) is the deformable derivative of y, 0 < α < 1. we use weissinger’s fixed point theorem and krasnoselskii’s fixed point theorem to achieve our main results. an example is provided for illustration.