Results 271 to 280 of about 6,876 (298)

Finite Fractional Sturm–Liouville Transforms For Generalized Fractional Derivatives

Iranian Journal of Science and Technology, Transactions A: Science, 2017
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Eshaghi, Shiva, Ansari, Alireza
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A generalized local fractional derivative with applications

Journal of Computational Physics
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Sroor M. Elnady, Mohamed El-Beltagy, Ahmed G. Radwan, Mohammed E. Fouda   +3 more
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Novel Results on Legendre Polynomials in the Sense of a Generalized Fractional Derivative

Mathematical and Computational Applications
In this article, new results are investigated in the context of the recently introduced Abu-Shady–Kaabar fractional derivative. First, we solve the generalized Legendre fractional differential equation.
FRANCISCO Martinez, Mohammed K A Kaabar, Kaabar Mohammed K A   +2 more
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General fractional integrals and derivatives and their applications

Physica D: Nonlinear Phenomena, 2023
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A Numerical Scheme for a Generalized Fractional Derivative with Variable Order

2023
The aim of this paper is to present an approximation formula for the Caputo fractional derivative of variable order, with dependence on an arbitrary kernel. For special cases of this kernel function, or the fractional order being constant, we recover some known formulas.
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Taylor’s Series Generalized for Fractional Derivatives and Applications

SIAM Journal on Mathematical Analysis, 1971
The familiar Taylor’s series expansion of the function , $f(z)$ has for its general term $D^n f(z_0 ){{(z - z_0 )^n } / {n!}}$. A new generalization of Taylor’s series in which the general term is $D^{an + \gamma } f(z_0 ){{(z - z_0 )^{an + \gamma } } / {\Gamma (an + \gamma + 1)}}$, where $a > 0$ and $\gamma $ is an arbitrary complex number, is ...
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Generation of optical vortices by fractional derivative

Optics and Lasers in Engineering, 2014
Abstract This paper presents a new method of vortex generation using two-dimensional fractional derivative. The characteristics of vortices obtained using this method from Gaussian and Hermite–Gauss distributions are presented. Changing the parameters of fractional derivative such as the fractional order, r, and the direction, θ, the positions of the
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Fractional derivatives: integral representations and generalized polynomials

2004
Summary: We show that the use of functions associated with generalized forms of Hermite polynomials provide a natural tool for the solution of partial differential equations involving fractional derivatives. Within such a context we clarify the meaning of exponential operators with fractional derivatives and discuss alternative definitions based on ...
DATTOLI G, CESARANO C, RICCI, Paolo Emilio, VAZQUEZ L.   +3 more
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A new approximation for the generalized fractional derivative and its application to generalized fractional diffusion equation

Numerical Methods for Partial Differential Equations, 2021
Qinxu Ding, Patricia J Y Wong
exaly  

On Some Generalizations of the Bi-Ordinal Hilfer’s Fractional Derivative

Cybernetics and Systems Analysis
The article is devoted to the generalization of the concept of bi-ordinal Hilfer’s fractional derivative, previously introduced in an author’s work. In particular, the concept of the bi-ordinal Hilfer’s derivative of a function with respect to another function and proportional bi-ordinal Hilfer derivative of a function with respect to another function ...
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