Continuous time random walk to a general fractional Fokker–Planck equation on fractal media
A general fractional calculus is described using fractional operators with respect to another
function, and some often used propositions are presented in this framework. Together with …
function, and some often used propositions are presented in this framework. Together with …
A note on function space and boundedness of the general fractional integral in continuous time random walk
Q Fan, GC Wu, H Fu - Journal of Nonlinear Mathematical Physics, 2022 - Springer
The general fractional calculus becomes popular in continuous time random walk recently.
However, the boundedness condition of the general fractional integral is one of the …
However, the boundedness condition of the general fractional integral is one of the …
On tempered Hilfer fractional derivatives with respect to functions and the associated fractional differential equations
We investigate the Hilfer-type operator within the topic of tempered fractional calculus with
respect to functions. This operator, the tempered Ψ-Hilfer derivative, is defined for the first …
respect to functions. This operator, the tempered Ψ-Hilfer derivative, is defined for the first …
Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations
HM Fahad, A Fernandez - Applied Mathematics and Computation, 2021 - Elsevier
Mikusiński's operational calculus is a method for interpreting and solving fractional
differential equations, formally similar to Laplace transforms but more rigorously justified …
differential equations, formally similar to Laplace transforms but more rigorously justified …
On tempered fractional calculus with respect to functions and the associated fractional differential equations
The prime aim of the present paper is to continue developing the theory of tempered
fractional integrals and derivatives of a function with respect to another function. This theory …
fractional integrals and derivatives of a function with respect to another function. This theory …
Weighted fractional calculus: a general class of operators
A Fernandez, HM Fahad - Fractal and Fractional, 2022 - mdpi.com
We conduct a formal study of a particular class of fractional operators, namely weighted
fractional calculus, and its extension to the more general class known as weighted fractional …
fractional calculus, and its extension to the more general class known as weighted fractional …
On Laplace transforms with respect to functions and their applications to fractional differential equations
An important class of fractional differential and integral operators is given by the theory of
fractional calculus with respect to functions, sometimes called Ψ‐fractional calculus. The …
fractional calculus with respect to functions, sometimes called Ψ‐fractional calculus. The …
Scale-invariant general fractional calculus: Mellin convolution operators
VE Tarasov - Fractal and Fractional, 2023 - mdpi.com
General fractional calculus (GFC) of operators that is defined through the Mellin convolution
instead of Laplace convolution is proposed. This calculus of Mellin convolution operators …
instead of Laplace convolution is proposed. This calculus of Mellin convolution operators …
Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator
X Zhang, P Chen, H Tian, Y Wu - Fractal and Fractional, 2023 - mdpi.com
In this paper, we consider the existence of positive solutions for a singular tempered
fractional equation with ap-Laplacian operator. By constructing a pair of suitable upper and …
fractional equation with ap-Laplacian operator. By constructing a pair of suitable upper and …
On the importance of conjugation relations in fractional calculus
A Fernandez, HM Fahad - Computational and Applied Mathematics, 2022 - Springer
It is useful to understand how the various operators of fractional calculus relate to each
other, especially relations between newly defined operators and classical well-studied ones …
other, especially relations between newly defined operators and classical well-studied ones …