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Recently, a new fractional derivative called the conformable fractionalderivative is given on based basic limit definition derivative in [4]. Then,the fractional versions of chain rules, exponential functions, Gronwallsinequality, integration by parts, Taylor power series expansions is developedin [5]. In this paper, we present existence and uniqueness theorems forsequential linear conformable fractional differential equations.

Existence and Uniqueness Theorems for Sequential Linear Conformable Fractional Differential Equations