Analytic study for a fractional model of HIV infection of C D 4 + T lymphocyte cells

Abstract

In this article, we implemented homotopy transform methods, namely, homotopy analysis transform method and homotopy perturbation Sumudu transform method to examine the fractional model for HIV infection of CD4 + T lymphocyte cells. Proliferation of CD4 + T lymphocyte cells is driven by a combination of the homeostatic response to cells depletion (CD4 + T cells counts) and viral load (HIV levels). The attraction of both the methods is that an approach of HPSTM is used and on other hand by HATM a large admissible convergence range of series solution is described for standard as well as fractional order nonlinear problems.

Two novel computational techniques for fractional Gardner and Cahn‐Hilliard equations

“…The HAM has been effectively aided to find the solution for problems arises in connected areas of science and technology. Recently, many authors study the different phenomena situated in different areas with the help of q-HATM, such as Srivastava et al studied the model of vibration equation of arbitrary order, 50 Singh et al are employed to find the solution for advection-dispersion equation, 51 Bulut et al analyze HIV infection of CD4 + T lymphocyte cells of fractional model, 52 Veeresha et al find the solution for fractional KdV-Burgers equation, 53 Kumar et al analyze the model of Lienard's equation, 54 and many others. Recently, many authors study the different phenomena situated in different areas with the help of q-HATM, such as Srivastava et al studied the model of vibration equation of arbitrary order, 50 Singh et al are employed to find the solution for advection-dispersion equation, 51 Bulut et al analyze HIV infection of CD4 + T lymphocyte cells of fractional model, 52 Veeresha et al find the solution for fractional KdV-Burgers equation, 53 Kumar et al analyze the model of Lienard's equation, 54 and many others.…”

“…Furthermore, q-HATM was proposed by Singh et al, 49 which is an elegant amalgamation of q-HAM and LT. Recently, many authors study the different phenomena situated in different areas with the help of q-HATM, such as Srivastava et al studied the model of vibration equation of arbitrary order, 50 Singh et al are employed to find the solution for advection-dispersion equation, 51 Bulut et al analyze HIV infection of CD4 + T lymphocyte cells of fractional model, 52 Veeresha et al find the solution for fractional KdV-Burgers equation, 53 Kumar et al analyze the model of Lienard's equation, 54 and many others. [55][56][57][58] To present the fundamental idea of q-HATM, we consider a fractional-order nonlinear partial differential equation of the form…”

A reliable technique for fractional modified Boussinesq and approximate long wave equations

“…Consider the modified Boussinesq (MB) equations of fractional order [15,17,20]: (26) with initial conditions . 9 Coupled surface of and for Ex.…”

“…Recently, due to consistency and efficacy of -HATM it has been eminently aided by many researchers to analyse various kinds of nonlinear problem like, authors in [23] analysed and find the approximated analytical solution for fractional model of vibration equation and elucidate the exactness of -HATM, in [24] the solution for fractional Drinfeld-Sokolov-Wilson equation has been investigated by the aid of proposed scheme, the cancer chemotherapy effect model with fractional order has been analysed by the authors in [25], H. Bulut and his co-authors analyse HIV infection of CD4+T lymphocyte cells of fractional model [26], the efficiency of considered algorithm is presented while finding the solution for fractional telegraph equation equation in [27], authors in [28] analysed the model of Lienard's equation, and many others has study and find the solution for many complex problems arised in related fields of science [29][30][31][32][33][34]. Motivated by these investigations, we find the approximated analytical solution for coupled DEs describing the shallow water waves through distinct dispersion relation.…”

Using Difference Scheme Method to the Fractional Telegraph Model with Atangana-Baleanu-Caputo Derivative

“…Over the last several decades, many scientists and experts are turning their studies into real world problems. This trend comes from new and novel structures of models to the real world problems and the application of di¤erential equations with fractional derivative [1,2,3,4]. Therefore, many fractional theorems and de…nitions in the sense of Rimann-Liouville, Caputo, Atangana-Baleanu have been introduced to the literature.…”