Search
Search Results
-
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...
-
Abstract Algebraic Construction in Fractional Calculus: Parametrised Families with Semigroup Properties
What structure can be placed on the burgeoning field of fractional calculus with assorted kernel functions? This question has been addressed by the...
-
Elements of Fractional Calculus
This chapter is devoted to introducing the elements of fractional calculus, Fractional calculusemphasizing some aspects of the historical development...
-
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...
-
Calculus of variations with higher order Caputo fractional derivatives
In this work, we consider fractional variational problems depending on higher order fractional derivatives. We obtain optimality conditions for such...
-
Refinements of Local Fractional Hilbert-Type Inequalities
We study the refinements of several well-known local fractional Hilbert-type inequalities obtained by interpolating the Lebesgue norms of local...
-
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition
Nonlocal vector calculus, which is based on the nonlocal forms of gradient, divergence, and Laplace operators in multiple dimensions, has shown...
-
Mathematical Foundation of Fractional Calculus
In the long history of the development of fractional calculus, a variety of definitions have been proposed by researchers from different...
-
Towards a Unified theory of Fractional and Nonlocal Vector Calculus
Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are...
-
Generalized Mellin transform and its applications in fractional calculus
In this paper, we introduce a generalized Mellin transform in the framework of fractional operators with respect to functions. The generalized Mellin...
-
Spatiotemporal linear stability of viscoelastic subdiffusive channel flows: a fractional calculus framework
The temporal and spatiotemporal linear stability analyses of viscoelastic, subdiffusive, plane Poiseuille flow obeying the Fractional Upper Convected...
-
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...
-
A Local Discontinuous Galerkin Method for Time-Fractional Diffusion Equations
In this paper, a local discontinuous Galerkin (LDG) scheme for the time-fractional diffusion equation is proposed and analyzed. The Caputo...
-
A novel computational approach to the local fractional Lonngren wave equation in fractal media
The main purpose of this paper is to investigate the local fractional Lonngren wave equation, which is a generalization of Lonngren wave equation in...
-
On variable-order fractional linear viscoelasticity
A generalization of fractional linear viscoelasticity based on Scarpi’s approach to variable-order fractional calculus is presented. After reviewing...
-
Two-weight Norm Inequalities for Local Fractional Integrals on Gaussian Measure Spaces
In this paper, the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian...
-
Fractal and Fractional Calculus
It has been 2000 years since the third century BC, when Euclidean geometry was established by Euclid. This system has been considered as a definite,...
-
Fractional Bessel Derivative Within the Mellin Transform Framework
In this paper, we present a fresh perspective on the fractional power of the Bessel operator using the Mellin transform. Drawing inspiration from the...