Results 21 to 30 of about 201,097 (279)

Symmetry Analysis of Initial and Boundary Value Problems for Fractional Differential Equations in Caputo sense [PDF]

, 2019
In this work we study Lie symmetry analysis of initial and boundary value problems for partial differential equations (PDE) with Caputo fractional derivative.
Iskenderoglu, Gulistan, Kaya, Dogan
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Aging and Rejuvenation with Fractional Derivatives [PDF]

, 2004
We discuss a dynamic procedure that makes the fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and ...
B. J. West, Bruce J. West, D. Bedeaux, E. W. Montroll, F. Bardou, Gerardo Aquino, Mauro Bologna, Paolo Grigolini, R. Kubo   +8 more
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Fuzzy Generalized Conformable Fractional Derivative

Advances in Fuzzy Systems, 2020
We give a new definition of fuzzy fractional derivative called fuzzy conformable fractional derivative. Using this definition, we prove some results and we introduce new definition of generalized fuzzy conformable fractional derivative.
Atimad Harir, Said Melliani, Lalla Saadia Chadli   +2 more
doaj   +1 more source

An analytical solution for the Caputo type generalized fractional evolution equation

Alexandria Engineering Journal, 2022
The Caputo type generalized fractional evolution equation is studied in this paper. Since the Caputo type generalized fractional derivative is well-known for being the generalization of Caputo fractional derivatives, this article’s studies contribute to ...
Wannika Sawangtong, Panumart Sawangtong
doaj   +1 more source

Coupled systems of fractional equations related to sound propagation: analysis and discussion [PDF]

, 2012
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in the ...
Diethelm K., Federico Polito, Fellah Z. E. A., Haubold H. J., Kilbas A. A., Podlubny I., Roberto Garra   +6 more
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Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus

Entropy, 2023
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry.
Airton Deppman, Eugenio Megías, Roman Pasechnik   +2 more
doaj   +1 more source

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

Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations

Journal of Advanced Research, 2023
Introduction: Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement ...
Mohammad Hossein Heydari, Mohsen Razzaghi, Dumitru Baleanu   +2 more
doaj   +1 more source

On Hilfer generalized proportional fractional derivative

Advances in Difference Equations, 2020
Motivated by the Hilfer and the Hilfer–Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann–Liouville and Caputo generalized proportional fractional ...
Idris Ahmed, Poom Kumam, Fahd Jarad, Piyachat Borisut, Wachirapong Jirakitpuwapat   +4 more
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Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform

Fractal and Fractional, 2023
In this paper, the Kharrat–Toma transforms of the Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and the regularized version of the HP fractional derivative are derived.
Ved Prakash Dubey, Jagdev Singh, Sarvesh Dubey, Devendra Kumar   +3 more
doaj   +1 more source