Abstract
Abstract In this article, more general types of fractional proportional integrals and derivatives are proposed. Some properties of these operators are discussed.
Highlights
The fractional calculus, which is engaged in integral and di erential operators of arbitrary orders, is as old as the conceptional calculus that deals with integrals and derivatives of non-negative integer orders
It turned out that the fractional operators are excellent tools to use in modeling long-memory processes and many phenomena that appear in physics, chemistry, electricity, mechanics and many other disciplines
The fractional integrals and derivatives which were proposed in these works were just particular cases of what so called fractional integrals/derivatives withe dependence on a kernel function [2, 5, 17]
Summary
The fractional calculus, which is engaged in integral and di erential operators of arbitrary orders, is as old as the conceptional calculus that deals with integrals and derivatives of non-negative integer orders. Abstract: In this article, more general types of fractional proportional integrals and derivatives are proposed. We extend the work done in [32] to introduce a new fractional operators relying on the proportional derivatives of a function with respect to another function which can be de ned in parallel with the de nitions discussed in [30].
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