Gronwall type inequality on generalized fractional conformable integral operators

Abstract

Abstract In 2015, Abdeljawad defined the conformable fractional derivative (Grunwald–Letnikov technique) to iterate the conformable fractional integral of order 0 < α ≤ 1 {0<\alpha\leq{1}} (Riemann approach), yielding Hadamard fractional integrals when α = 0 {\alpha=0} . The Gronwall type inequality for generalized operators unifying Riemann–Liouville and Hadamard fractional operators is obtained in this study. We use this inequality to show how the order and initial conditions affect the solution of differential equations with generalized fractional derivatives. More features for generalized fractional operators are established, as well as solutions to initial value problems in several new weighted spaces of functions.