A new fractional derivative and its fractional integral with some\n example

A new derivative, called deformable derivative, is introduced here which is\nequivalent to ordinary derivative in the sense that one implies other. The\ndeformable derivative is defined using limit approach like that of ordinary one\nbut with respect to a parameter varying over unit interval. Thus it could also\nbe regarded as a fractional derivative. Reason of calling it as deformable\nderivative is because of its intrinsic property of continuously deforming\nfunction to derivative. This is substantiated by its linear connection to\nfunction and its derivative. Besides discussing some of its basic properties,\nwe discover the forms of Rolle's, Mean Value and Taylor's theorems. The\nfundamental theorem of calculus for this fractional derivative could be taken\nas definition of its fractional integral. As a theoretical application some\nfractional differential equations are solved.\n