The Non-Newtonian calculus is inspired by the homeomorphism from the real line to the open interval that we denote it by α(x). This function modifies the preliminary algebraic operators and the new fractional differintegration formula will be found. On the other hand, the Ψ-fractional calculus was introduced in the aid of generalized Leibniz formula for production of two differentiable functions which has been driven to the similar fractional operators. In this literature the relationship between these two operators are investigated and new interpretation of Ψ-fractional calculus is studied.
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