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We obtain in this article a solution of sequential differential equation involving the Hadamard fractional derivative and focusing the orders in the intervals (1,2) and (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.doi:10.1155/2018/9605353 fatcat:uty7lq5zbje55nkqm3rfiuczjq