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In this paper, we propose and prove some new results on the recently proposed conformable fractional derivatives and fractional integral, [Khalil, R., et al., A new definition of fractional derivative, J. Comput. Appl. Math. 264, (2014)]. The simple nature of this definition allows for many extensions of some classical theorems in calculus for which the applications are indispensable in the fractional differential models that the existing definitions do not permit. The extended mean value theorem and the Racetrack type principle are proven for the class of functions which are a-differentiable in the context of conformable fractional derivatives and fractional integral. We also apply the D’Alambert approach to the conformable fractional differential equation of the form: Ta Ta y+ pTa y+qy = 0, where p and q are a−differentiable functions as application.

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