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.
"Laplace Transform, Gronwall Inequality and Delay Differential Equations for General Conformable Fractional Derivative." Commun. Math. Anal. 22 (1) 14 - 33, 2019.