A tumor is most dangerous disease of medical science which is a mass or lumps of tissue that’s formed by an accumulation of abnormal cells. A famous fractional tumor-immune model is interpreting the dynamics of tumor and effector cells. In this work, we provide a comparative and chaotic study of tumor and effector cells through fractional tumor-immune dynamical model. A new arbitrary operator based on the Mittag-Leffler law is assumed for this study. Again, we examine the interactions among distinct tumor cell inhabitants and immune structure through a model of real world problem of medical science. We First investigate the dynamical effect of the activation of the effector immune and tumor cells by using Adams-Bashforth-Moulton and Toufik-Atangana methods. Furthermore, this paper analyses the existence and uniqueness of given tumor-immune model of arbitrary order. Further, we have examined the dynamical behaviors of the fractional tumor-immunne model and obtained results are compared with exiting results by other methods. Numerical simulations are executed by Adams-Bashforth-Moulton and Toufik-Atangana methods using popular Atangana-Baleanu fractional derivative. Our obtained results will be useful for biologists to the treatment of cancer disease.

A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment

This work finds several new traveling wave solutions for nonlinear directional couplers with optical metamaterials by means of the modified Kudryashov method. This model can be used to distribute light from a main fiber into one or more branch fibers. Two forms of optical couplers are considered, namely the twin- and multiple- core couplers. These couplers, which have applications as intensity-dependent switches and as limiters, are studied with four nonlinear items namely the Kerr, power, parabolic, and dual-power laws. The restrictions on the parameters for the existence of solutions are also examined. The 3D- and 2D figures are introduced to discuss the physical meaning for some of the gained solutions. The performance of the used method shows the adequate, power, and ability for applying to many other nonlinear evolution models.

https://iopscience.iop.org/article/10.1088/1402-4896/ab95af/pdf

Traveling wave solutions to nonlinear directional couplers by modified Kudryashov method

https://iopscience.iop.org/article/10.1088/1572-9494/ab6181/pdf

Investigation of soliton solutions with different wave structures to the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation

This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

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Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

Analytical and numerical study of the HIV-1 infection of CD4+ T-cells conformable fractional mathematical model that causes acquired immunodeficiency syndrome with the effect of antiviral drug therapy

In this work, the KdV equation with conformable derivative and dual-power law nonlinearity is considered. It is exceedingly used as a model to depict the feeble nonlinear long waves in different fields of sciences. Furthermore, it explains the comparable effects of weak dispersion and weak nonlinearity on the evolvement of the nonlinear waves. Using the Jacobi elliptic function expansion method, new exact solutions of that equation have been found. As results, some obtained solutions behave as periodic traveling waves, bright soliton, and dark soliton.

Franoosh Izadi

Papers

Jacobi Elliptic Function Expansion Method for Solving KdV Equation with Conformable Derivative and Dual-Power Law Nonlinearity