Results 71 to 80 of about 12,535 (181)

General Fractional Calculus Operators of Distributed Order

Axioms, 2023
In this paper, two types of general fractional derivatives of distributed order and a corresponding fractional integral of distributed type are defined, and their basic properties are investigated.
Mohammed Al-Refai, Yuri Luchko
doaj   +1 more source

A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies

Entropy, 2021
Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods
Hua Wang, Hadi Jahanshahi, Miao-Kun Wang, Stelios Bekiros, Jinping Liu, Ayman A. Aly   +5 more
doaj   +1 more source

A new crossover dynamics mathematical model of monkeypox disease based on fractional differential equations and the Ψ-Caputo derivative: Numerical treatments

Alexandria Engineering Journal
A novel crossover model for monkeypox disease that incorporates Ψ-Caputo fractional derivatives is presented here, where we use a simple nonstandard kernel function Ψ(t).
N.H. Sweilam, S.M. Al-Mekhlafi, W.S. Abdel Kareem, G. Alqurishi   +3 more
doaj   +1 more source

A survey on fractional variational calculus

, 2018
Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods.
Almeida, Ricardo, Torres, Delfim F. M.
core   +1 more source

Exact results for a fractional derivative of elementary functions

SciPost Physics, 2018
We present exact analytical results for the Caputo fractional derivative of a wide class of elementary functions, including trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic, Gaussian, quartic Gaussian, and Lorentzian ...
Gavriil Shchedrin, Nathanael C. Smith, Anastasia Gladkina, Lincoln D. Carr
doaj   +1 more source

Boundary Conditions for Fractional Diffusion

, 2017
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state ...
Baeumer, Boris, Kovács, Mihály, Meerschaert, Mark M., Sankaranarayanan, Harish   +3 more
core   +1 more source

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

Numerical approximations of groundwater flow problem using fractional variational iteration method with fractional derivative of singular and nonsingular kernels

International Journal of Mathematics for Industry
This study aims to present the numerical approximations of groundwater flow problem, namely the time-fractional Boussinesq equation using the fractional variational iteration method.
Pravindra Kumar, Mahaveer Prasad Yadav
doaj   +1 more source

On uniform stability and numerical simulations of complex valued neural networks involving generalized Caputo fractional order

Scientific Reports
The dynamics and existence results of generalized Caputo fractional derivatives have been studied by several authors. Uniform stability and equilibrium in fractional-order neural networks with generalized Caputo derivatives in real-valued settings ...
Sumati Kumari Panda, Thabet Abdeljawad, A. M. Nagy   +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