On the formulation and numerical simulation of distributed-order fractional optimal control problems

MA Zaky, JAT Machado - … in Nonlinear Science and Numerical Simulation, 2017 - Elsevier
In a fractional optimal control problem, the integer order derivative is replaced by a fractional
order derivative. The fractional derivative embeds implicitly the time delays in an optimal …

Spectral technique for solving variable‐order fractional Volterra integro‐differential equations

EH Doha, MA Abdelkawy, AZM Amin… - Numerical Methods for …, 2018 - Wiley Online Library
This article, presented a shifted Legendre Gauss‐Lobatto collocation (SL‐GL‐C) method
which is introduced for solving variable‐order fractional Volterra integro‐differential equation …

Modified Galerkin algorithm for solving multitype fractional differential equations

MM Alsuyuti, EH Doha, SS Ezz‐Eldien… - … methods in the …, 2019 - Wiley Online Library
The primary point of this manuscript is to dissect and execute a new modified Galerkin
algorithm based on the shifted Jacobi polynomials for solving fractional differential …

Fast and precise spectral method for solving pantograph type Volterra integro-differential equations

SS Ezz-Eldien, EH Doha - Numerical Algorithms, 2019 - Springer
This paper focuses on studying a general form of pantograph type Volterra integro-
differential equations (PVIDEs). We apply a new collocation spectral approach, based on …

Shifted Jacobi–Gauss-collocation with convergence analysis for fractional integro-differential equations

EH Doha, MA Abdelkawy, AZM Amin… - … in Nonlinear Science and …, 2019 - Elsevier
A new shifted Jacobi–Gauss-collocation (SJ-GC) algorithm is presented for solving
numerically several classes of fractional integro-differential equations (FI-DEs), namely …

[HTML][HTML] Barycentric interpolation collocation methods for solving linear and nonlinear high-dimensional Fredholm integral equations

H Liu, J Huang, Y Pan, J Zhang - Journal of Computational and Applied …, 2018 - Elsevier
In this article two barycentric interpolation collocation methods are proposed for solving
linear and nonlinear high-dimensional F redholm integral equations of the second kind. The …

On spectral methods for solving variable-order fractional integro-differential equations

EH Doha, MA Abdelkawy, AZM Amin… - … and Applied Mathematics, 2018 - Springer
This paper applies the shifted Jacobi–Gauss collocation (SJ–GC) method for solving
variable-order fractional integro-differential equations (VO-FIDE) with initial conditions. The …

Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations

EHH Doha, MAA Abdelkawy, AZ Amin… - … Analysis: Modelling and …, 2019 - zurnalai.vu.lt
This article addresses the solution of multi-dimensional integro-differential equations (IDEs)
by means of the spectral collocation method and taking the advantage of the properties of …

Approximate solution of nonlinear Fredholm integral equations of the second kind using a class of Hermite interpolation polynomials

N Karamollahi, M Heydari, GB Loghmani - Mathematics and Computers in …, 2021 - Elsevier
A particular case of the Hermite interpolation method, namely the two-point Taylor formula, is
utilized to construct a numerical technique for solving Fredholm integral equations (FIEs) of …

Meshfree approach for solving multi-dimensional systems of Fredholm integral equations via barycentric Lagrange interpolation

H Liu, J Huang, W Zhang, Y Ma - Applied Mathematics and Computation, 2019 - Elsevier
A highly accurate meshfree approach based on the barycentric Lagrange basis functions is
reported for solving the linear and nonlinear multi-dimensional systems of Fredholm integral …