On the fractional-order model of HIV-1 infection of CD4+ T-cells under the influence of antiviral drug treatment

R Ullah, R Ellahi, SM Sait… - Journal of Taibah …, 2020 - Taylor & Francis
In this article, the fractional-order model, namely HIV-1 infection of CD4+ T-cells combined
with the effect of antiviral drug treatment, is investigated. The model includes three unknown …

Numerical solutions of fractional advection–diffusion equations with a kind of new generalized fractional derivative

Y Xu, Z He, Q Xu - International Journal of Computer Mathematics, 2014 - Taylor & Francis
In the current paper, the numerical solutions for a class of fractional advection–diffusion
equations with a kind of new generalized time-fractional derivative proposed last year are …

The natural transform decomposition method for linear and nonlinear partial differential equations.

HM Baskonus, H Bulut, Y Pandir - … in Engineering, Science & …, 2014 - search.ebscohost.com
In this paper, we study the analytical solutions of linear and nonlinear partial differential
equations by Natural Transform Decomposition Method (NTDM) which is formed by …

Numerical solutions and analysis of diffusion for new generalized fractional advection-diffusion equations

Y Xu, OP Agrawal - Central European Journal of Physics, 2013 - Springer
In this paper we study a class of new Generalized Fractional Advection-Diffusion Equations
(GFADEs) with a new Generalized Fractional Derivative (GFD) proposed last year. The new …

Numerical schemes for fractional optimal control problems

A Alizadeh, S Effati, A Heydari - Journal of …, 2017 - asmedigitalcollection.asme.org
In the present study, variational iteration and Adomian decomposition methods (ADMs) are
applied for solving a class of fractional optimal control problems (FOCPs). Also, a …

[PDF][PDF] A comparative study between semi-analytical iterative schemes for the reliable treatment of systems of coupled nonlinear partial differential equations

L Ebiwareme - International Journal of Innovation Engineering and …, 2022 - ijiesr.com
This study is aimed at making comparative analysis between three semi-analytical iterative
methods viz: Adomian decomposition method, Temimi-Ansari method and Daftardar-Jafari …

Non-probabilistic solutions of imprecisely defined fractional-order diffusion equations

S Chakraverty, S Tapaswini - Chinese Physics B, 2014 - iopscience.iop.org
The fractional diffusion equation is one of the most important partial differential equations
(PDEs) to model problems in mathematical physics. These PDEs are more practical when …

Legendre‐Spectral Algorithms for Solving Some Fractional Differential Equations

YH Youssri, WM Abd‐Elhameed - Fractional Order Analysis …, 2020 - Wiley Online Library
This chapter is concerned with analyzing and presenting some algorithms for treating some
kinds of fractional differential equations (FDEs) based on utilizing some suitable spectral …

Fractional space–time nonlinear reaction–convection–diffusion

FS Costa, MRA Pereira - Computational and Applied Mathematics, 2018 - Springer
We comment the fractional space–time reaction–convection–diffusion defined by Grünwald–
Letnikov, Riesz and Riesz–Feller fractional derivatives. We find the explicit travelling wave …

[PDF][PDF] Approximation of ordinary fractional differential equations by differential equations with a small parameter

SY Lukashchuk - Vestnik Udmurtskogo Universiteta. Matematika …, 2017 - researchgate.net
S. Yu. Lukashchuk Approximation of ordinary fractional differential equations by differential
equations with a small parameter 2 Page 1 S. Yu. Lukashchuk Approximation of ordinary …