Elimination of the Nondifferentiation Problem and the Discontinuity Problem by the Conformable Definition.

Fractional calculus is now used in a variety of domains, including physics and engineering which have two problems in their study are the differentiation and the discontinuity problems. Hence, in this paper, we will present the conformable fractional derivative and integral. Then, we will use such definition and properties to construct functions that are differentiable in a fractional meaning but not differentiable in classical meaning at the point 0, then we will develop the construction of the mentioned kind functions at any point which will eliminate the first problem. Therefore, we will eliminate the second problem by approximate any given discontinuous function by its conformable fractional Fourier series which will be continuous and useful for the study that researchers need.