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On univariate fractional calculus with general bivariate analytic kernels
Several fractional integral and derivative operators have been defined recently with a bivariate structure, acting on functions of a single variable...
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On the analysis of fractional calculus operators with bivariate Mittag Leffler function in the kernel
Bivariate Mittag-Leffler (ML) functions are a substantial generalization of the univariate ML functions, which are widely recognized for their...
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A Geometric Based Connection between Fractional Calculus and Fractal Functions
Establishing the accurate relationship between fractional calculus and fractals is an important research content of fractional calculus theory. In...
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Some properties of bivariate Mittag-Leffler function
Our findings and discussions will add to the body of knowledge on Mittag-Leffler functions. A new extended bivariate Mittag-Leffler function is being...
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Katugampola Fractional Integral and Fractal Dimension of Bivariate Functions
The subject of this note is the mixed Katugampola fractional integral of a bivariate function defined on a rectangular region in the Cartesian plane....
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Fractional characteristic functions, and a fractional calculus approach for moments of random variables
In this paper we introduce a fractional variant of the characteristic function of a random variable. It exists on the whole real line, and is...
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On fractional calculus with analytic kernels with respect to functions
Many different types of fractional calculus have been proposed, which can be organised into some general classes of operators. For a unified...
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On a family of bivariate orthogonal functions
In this paper we investigate a family of bivariate orthogonal functions arising as a generalization of Koornwinder polynomials in two variables....
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Solving Prabhakar differential equations using Mikusiński’s operational calculus
We study the structure and operators of Prabhakar fractional calculus, in particular the operators of Caputo type, using the machinery of...
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Operational Calculus for the Riemann–Liouville Fractional Derivative with Respect to a Function and its Applications
Mikusiński’s operational calculus is a formalism for understanding integral and derivative operators and solving differential equations, which has...
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A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators
We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a...
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Dimensional Analysis of Mixed Riemann–Liouville Fractional Integral of Vector-Valued Functions
In this paper, we attempt to develop the concept of fractal dimension of the continuous bivariate vector-valued maps. We give few fundamental...
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On the variable order Weyl-Marchaud fractional derivative of non-affine fractal function
The fractal technique is applied to study a wide variety of phenomena in the universe. In particular, fractal techniques can be generalized through...
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Analyses of the Contour Integral Method for Time Fractional Normal-Subdiffusion Transport Equation
In this work, we theoretically and numerically discuss a class of time fractional normal-subdiffusion transport equation, which depicts a crossover...
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Fractional Brownian Motion
The previous chapters provide empirical evidence that models with stochastic volatility outperform their deterministic counterpart. In Chap....
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An effective computational solver for fractal-fractional 2D integro-differential equations
In this paper, we develop a computational approach for fractal-fractional integro-differential equations (FFIDEs) in Atangana–Riemann–Liouville...
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Application of the Fractional Sturm–Liouville Theory to a Fractional Sturm–Liouville Telegraph Equation
In this paper, we consider a non-homogeneous time–space-fractional telegraph equation in n -dimensions, which is obtained from the standard telegraph...
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Box dimension of mixed Katugampola fractional integral of two-dimensional continuous functions
The goal of this article is to study the box dimension of the mixed Katugampola fractional integral of two-dimensional continuous functions on
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An efficient numerical method based on Chelyshkov operation matrix for solving a type of time-space fractional reaction diffusion equation
In this article, a numerical method based on Chelyshkov operation matrix is built to investigate a time-space fractional reaction diffusion model....
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An efficient parametric finite difference and orthogonal spline approximation for solving the weakly singular nonlinear time-fractional partial integro-differential equation
In this paper, a numerical method is presented to solve a nonlinear weakly singular time-fractional partial integro–differential equation with Caputo...
