Results 91 to 100 of about 388,923 (185)

Remarks on Sequential Caputo Fractional Differential Equations with Fractional Initial and Boundary Conditions

Mathematics
In the literature so far, for Caputo fractional boundary value problems of order 2q when ...
Aghalaya S. Vatsala, Bhuvaneswari Sambandham   +1 more
doaj   +1 more source

Approximations for the Caputo Derivative (I)

, 2016
In this paper we construct approximations for the Caputo derivative of order $1-α,2-α,2$ and $3-α$. The approximations have weights $0.5\left((k+1)^{-α}-(k-1)^{-α}\right)/Γ(1-α)$ and $k^{-1-α}/Γ(-α)$, and the higher accuracy is achieved by modifying the initial and last weights using the expansion formulas for the left and right endpoints.
openaire   +2 more sources

A New Extension of Extended Caputo Fractional Derivative Operator

, 2018
Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional
Gauhar Rahman, Shahid Mubeen, Kottakkaran Sooppy Nisar   +2 more
core   +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

Stability of solutions to impulsive Caputo fractional differential equations

Electronic Journal of Differential Equations, 2016
Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation ...
Ravi Agarwal, Snezhana Hristova, Donal O'Regan   +2 more
doaj  

Galerkin Finite Element Method for Caputo–Hadamard Time-Space Fractional Diffusion Equation

Mathematics
In this paper, we study the Caputo–Hadamard time-space fractional diffusion equation, where the Caputo derivative is defined in the temporal direction and the Hadamard derivative is defined in the spatial direction separately.
Zhengang Zhao, Yunying Zheng
doaj   +1 more source

A study of forced oscillations via Hilfer fractional derivative

CQD Revista Eletrônica Paulista de Matemática, 2022
The present study seeks to understand the forced oscillations through modeling via fractional differential equation, using the derivative according to Hilfer and representing the external force as a succession of delta Dirac functions.
Silas de Sá Cavalcanti Melo, Edmundo Capelas de Oliveira   +1 more
doaj  

Approximation of hamilton-jacobi equations with the caputo time-fractional derivative [PDF]

, 2020
We investigate the numerical approximation of Hamilton-Jacobi equations with the Caputo time-fractional derivative. We introduce an explicit in time discretization of the Caputo derivative and a finite difference scheme for the approximation of the ...
Camilli, Fabio, Duisembay, Serikbolsyn
core  

Approximation of Hamilton-Jacobi equations with Caputo time-fractional derivative

, 2020
In this paper, we investigate the numerical approximation of Hamilton-Jacobi equations with the Caputo time-fractional derivative. We introduce an explicit in time discretization of the Caputo derivative and a finite difference scheme for the ...
Fabio Camilli, Serik Duisembay
core  

Solvability of Fractional Boundary Value Problems for a Combined Caputo Derivative

, 2021
This paper deals with a class of boundary value problems of fractional differential equations involving the combined Caputo derivative, which can reflect both the past and the future nonlocal memory effects.
Toprakseven, ŞUAYİP
core