Applications of distributed-order fractional operators: A review
Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader
area of fractional calculus that has important and far-reaching applications for the modeling …
area of fractional calculus that has important and far-reaching applications for the modeling …
A review of operational matrices and spectral techniques for fractional calculus
AH Bhrawy, TM Taha, JAT Machado - Nonlinear Dynamics, 2015 - Springer
Recently, operational matrices were adapted for solving several kinds of fractional
differential equations (FDEs). The use of numerical techniques in conjunction with …
differential equations (FDEs). The use of numerical techniques in conjunction with …
[HTML][HTML] A new Jacobi operational matrix: an application for solving fractional differential equations
In this paper, we derived the shifted Jacobi operational matrix (JOM) of fractional derivatives
which is applied together with spectral tau method for numerical solution of general linear …
which is applied together with spectral tau method for numerical solution of general linear …
A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations
In this paper, an efficient and accurate spectral numerical method is presented for solving
second-, fourth-order fractional diffusion-wave equations and fractional wave equations with …
second-, fourth-order fractional diffusion-wave equations and fractional wave equations with …
Two analytical methods for time-fractional nonlinear coupled Boussinesq–Burger's equations arise in propagation of shallow water waves
In this paper, an analytical method based on the generalized Taylors series formula together
with residual error function, namely residual power series method (RPSM), is proposed for …
with residual error function, namely residual power series method (RPSM), is proposed for …
Solving differential equations of fractional order using an optimization technique based on training artificial neural network
M Pakdaman, A Ahmadian, S Effati… - Applied Mathematics …, 2017 - Elsevier
The current study aims to approximate the solution of fractional differential equations (FDEs)
by using the fundamental properties of artificial neural networks (ANNs) for function …
by using the fundamental properties of artificial neural networks (ANNs) for function …
Fractional spectral collocation methods for linear and nonlinear variable order FPDEs
M Zayernouri, GE Karniadakis - Journal of Computational Physics, 2015 - Elsevier
While several high-order methods have been developed for fractional PDEs (FPDEs) with
fixed order, there are no such methods for FPDEs with field-variable order. These equations …
fixed order, there are no such methods for FPDEs with field-variable order. These equations …
[HTML][HTML] A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation
This paper presents a direct solution technique for solving the generalized pantograph
equation with variable coefficients subject to initial conditions, using a collocation method …
equation with variable coefficients subject to initial conditions, using a collocation method …
A new numerical technique for solving the local fractional diffusion equation: two-dimensional extended differential transform approach
In this article, we first propose a new numerical technique based upon a certain two-
dimensional extended differential transform via local fractional derivatives and derive its …
dimensional extended differential transform via local fractional derivatives and derive its …