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In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also called proportional fractional operators of a function with respect to another function or proportional fractional operators with dependence on a kernel function.
In this article, a new definition of fractional Hilfer difference operator is introduced. Definition based properties are developed and utilized to construct fixed point operator for fractional order Hilfer difference equations with initial condition
Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications: Lebiniz rule an
Instead of the Ginsparg-Wilson (GW) relation we only require generalized chiral symmetry and show that this results in a larger class of Dirac operators describing massless fermions, which in addition to GW fermions and to the ones proposed by Fujika
This manuscript investigates the existence and uniqueness of solutions to the first order fractional anti-periodic boundary value problem involving Caputo-Katugampola (CK) derivative. A variety of tools for analysis this paper through the integral eq
This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the current time.