Deformable fractional derivative and its applications

In this paper, we introduce an application of recently proposed deformable derivative which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach as ordinary derivative. Thus it could also be regarded as fractional derivative. The simple nature of this definition allows us for the extension of some classical theorems in calculus like the Rolles, Mean Value and Extended Mean Value theorems. As a theoritical application some fractional differentiable equations are solved.