Solution of Sequential Hadamard Fractional Differential Equations by Variation of Parameter Technique

Abstract

We obtain in this article a solution of sequential differential equation involving the Hadamard fractional derivative and focusing the orders in the intervals $(\mathrm{1,2})$ and $(\mathrm{2,3})$. Firstly, we obtain the solution of the linear equations using variation of parameter technique, and next we investigate the existence theorems of the corresponding nonlinear types using some fixed-point theorems. Finally, some examples are given to explain the theorems.