Continuous dependence of a solution for fractional order Cauchy-type problem

Abstract

In this paper, we consider the generalized Cauchy-type problem involving Hilfer–Hadamard-type fractional derivative for the nonlinear fractional differential equations to study the continuous dependence of a solution on the general order under the initial conditions. Also, we present a slight generalization for the Gronwall inequality, which can be used in the study of the continuous dependence of the solution for the generalized Cauchy-type problem.

Keywords

• Generalized fractional Cauchy-type problem
• Hadamard-type
• Hilfer–Hadamard-type
• Nonlinear fractional differential equation
• Fractional derivatives
• Gronwall inequality