Gronwall type inequality on generalized fractional conformable integral operators (Q6603983)

In this paper the authors derived and proved the Gronwall inequality in the framework of generalized fractional integrals, which unifies the Riemann-Liouville and Hadamard fractional integrals. The results showed that the order and initial conditions affect the solution of differential equations with generalized fractional derivatives. In some special cases, the Gronwall inequality, Riemann-Liouville fractional operators and the Gronwall inequality for Hadamard fractional integrals were obtained. Furthermore, the initial value difficulties in the context of generalized fractional operators in some new weighted spaces of functions were also studied.