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Laplace Transform, Gronwall Inequality and Delay Differential Equations for General Conformable Fractional Derivative

Commun. Math. Anal.
Volume 22, Number 1 (2019), 14 - 33

Laplace Transform, Gronwall Inequality and Delay Differential Equations for General Conformable Fractional Derivative

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Abstract

In the present paper, the general conformable fractional derivative (GCFD) is considered and a corresponding Laplace transform is defined. Gronwall inequality is proved to show the exponential boundedness of a solution and using the Laplace transform the solution is found for certain classes of delay differential equations with GCFD.