Add to ORKGThe main goal of this paper is to construct a proportional analogues of the quaternionic fractional Fueter-type operator recently introduced in the literature. We start by establishing a quaternionic version of the well-known proportional fractional integral and derivative with respect to a real-valued function via the Riemann-Liouville fractional derivative. As a main result, we prove a quaternionic proportional fractional Borel-Pompeiu formula based on a quaternionic proportional fractional Stokes formula. This tool in hand allows us to present a Cauchy integral type formula for the introduced quaternionic proportional fractional Fueter-type operator with respect to a real-valued function.Comment: 20 page
Quaternion derivatives in the mathematical literature are typically defined only for analytic (regul...
The study of fractional integrals and fractional derivatives has a long history, and they have many ...
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. So...
Quaternionic analysis relies heavily on results on functions defined on domains in $\mathbb R^4$ (or...
The present paper is a continuation of our work [11], where we introduced a fractional operator calc...
Quaternionic analysis, it is usual to persist in pointing out to their distinguishedcharacteristics....
In this paper, we develop a fractional integro-differential operator calculus for Clifford-algebra v...
In the last three decades, fractional calculus has broken into the field of mathematical analysis, b...
We present a partial panoramic view of possible contexts and applications of the fractional calculus...
In recent years, fractional calculus has led to tremendous progress in various areas of science and ...
This article discusses a recently developed Mathematica tool -QPolynomial- a collection of functions...
Abstract: Based on the notion of fractional q–integral with the parametric lower limit of integratio...
Using the H-infinity-functional calculus for quaternionic operators, we show how to generate the fra...
During the past four decades or so, various operators of fractional calculus, such as those named af...
Abstract: In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we so...
Quaternion derivatives in the mathematical literature are typically defined only for analytic (regul...
The study of fractional integrals and fractional derivatives has a long history, and they have many ...
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. So...
Quaternionic analysis relies heavily on results on functions defined on domains in $\mathbb R^4$ (or...
The present paper is a continuation of our work [11], where we introduced a fractional operator calc...
Quaternionic analysis, it is usual to persist in pointing out to their distinguishedcharacteristics....
In this paper, we develop a fractional integro-differential operator calculus for Clifford-algebra v...
In the last three decades, fractional calculus has broken into the field of mathematical analysis, b...
We present a partial panoramic view of possible contexts and applications of the fractional calculus...
In recent years, fractional calculus has led to tremendous progress in various areas of science and ...
This article discusses a recently developed Mathematica tool -QPolynomial- a collection of functions...
Abstract: Based on the notion of fractional q–integral with the parametric lower limit of integratio...
Using the H-infinity-functional calculus for quaternionic operators, we show how to generate the fra...
During the past four decades or so, various operators of fractional calculus, such as those named af...
Abstract: In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we so...
Quaternion derivatives in the mathematical literature are typically defined only for analytic (regul...
The study of fractional integrals and fractional derivatives has a long history, and they have many ...
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. So...