Results 61 to 70 of about 161,465 (191)

Fractional Cauchy problems on bounded domains: survey of recent results

, 2010
In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. This problem was first considered by \citet{nigmatullin}, and \citet{zaslavsky} in $\mathbb R^d$ for modeling some physical phenomena.
A Einstein, AN Kochubei, AN Kochubei, AN Kochubei, AN Kochubei, B Baeumer, G Zaslavsky, Gilbarg D, Trudinger NS (2001) Elliptic partial differential equations of second order. Reprint of the, HL Royden, I Podlubny, J Bertoin, K Miller, KI Sato, M Caputo, M Naber, MM Meerschaert, MM Meerschaert, MM Meerschaert, MM Meerschaert, MM Meerschaert, MM Meerschaert, OP Agrawal, R Gorenflo, R Gorenflo, R Metzler, RF Bass, RR Nigmatullin, S Samko, W Arendt, WR Schneider   +29 more
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An efficient discrete Chebyshev polynomials strategy for tempered time fractional nonlinear Schrödinger problems

Journal of Advanced Research
Introduction: An interesting type of fractional derivatives that has received widespread attention in recent years is the tempered fractional derivatives. These fractional derivatives are a generalization of the well-known fractional derivatives, such as
Mohammad Hossein Heydari, Dumitru Baleanu   +1 more
doaj   +1 more source

Fractional differential equations solved by using Mellin transform

, 2014
In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin ...
Butera, Salvatore, Di Paola, Mario
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MR-Metric Spaces: Theory and Applications in Fractional Calculus and Fixed-Point Theorems [PDF]

Neutrosophic Sets and Systems
This paper investigates the interplay between MR-metric spaces and fractional calculus, estab lishing new theoretical results with applications in analysis and mathematical physics.
Abed Al-Rahman M. Malkawi, Ayat M. Rabaiah   +1 more
doaj   +3 more sources

Comparative study of integer-order and fractional-order artificial neural networks: Application for mathematical function generation

e-Prime: Advances in Electrical Engineering, Electronics and Energy
This paper investigates the impact of fractional derivatives on the activation functions of an artificial neural network (ANN). Based on the results and analysis, a three-layer backpropagation neural network model with fractional and integer derivatives ...
Manisha Premkumar Joshi, Savita Bhosale, Vishwesh A. Vyawahare   +2 more
doaj   +1 more source

Fractional Generalization of Gradient and Hamiltonian Systems

, 2005
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space.
Tarasov, Vasily E.
core   +2 more sources

Riemann’s conjecture and a fractional derivative

Computers & Mathematics with Applications, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Le Méhauté, A. El Kaabouchi, L. Nivanen   +2 more
openaire   +2 more sources

On Riemann-Liouville and Caputo Derivatives

Discrete Dynamics in Nature and Society, 2011
Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important properties of the Riemann-Liouville (
Changpin Li, Deliang Qian, YangQuan Chen
doaj   +1 more source

New Approach for Fractional Order Derivatives: Fundamentals and Analytic Properties

Mathematics, 2016
The rate of change of any function versus its independent variables was defined as a derivative. The fundamentals of the derivative concept were constructed by Newton and l’Hôpital.
Ali Karcı
doaj   +1 more source

Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions

, 2011
Using the Mellin transform approach, it is shown that, in contrast with integer-order derivatives, the fractional-order derivative of a periodic function cannot be a function with the same period.
Kaslik, Eva, Sivasundaram, Seenith
core   +1 more source