A general fractional formulation and tracking control for immunogenic tumor dynamics

Abstract

Mathematical modeling of biological systems is an important issue having significant effect on human beings. In this direction, the description of immune systems is an attractive topic as a result of its ability to detect and eradicate abnormal cells. Therefore, this manuscript aims to investigate the asymptotic behavior of immunogenic tumor dynamics based on a new fractional model constructed by the concept of general fractional operators. We discuss the stability and equilibrium points corresponding to the new model; then we modify the predictor–corrector method in general sense to implement the model and compare the associated numerical results with some real experimental data. As an achievement, the new model provides a degree of flexibility enabling us to adjust the complex dynamics of biological system under study. Consequently, the new general model and its solution method presented in this paper for the immunogenic tumor dynamics are new and comprise quite different information than the other kinds of classical and fractional equations. In addition to these, we implement a tracking control method in order to decrease the development of tumor‐cell population. The satisfaction of control purpose is confirmed by some simulation results since the controlled variables track the tumor‐free steady state in the whole realistic cases.

Design and analysis of a high order computational technique for time‐fractional Black–Scholes model describing option pricing

“…To acquire a fourth-order approximation of Equation ( 24), we further approximate w (4) (x m ) in (27). For this purpose, differentiating Equation ( 24) twice with respect to x and then rearranging the terms, we get…”

“…This is due to their wide‐range of applications in various fields of applied science and engineering. To mention few, the areas of applications of FDEs include signal processing, viscoelasticity, electrical network, continuum mechanics, material science and nuclear science, see in previous works 1–12 . Moreover, the FDEs were employed to model financial problems 13–15 …”

“…To mention few, the areas of applications of FDEs include signal processing, viscoelasticity, electrical network, continuum mechanics, material science and nuclear science, see in previous works. [1][2][3][4][5][6][7][8][9][10][11][12] Moreover, the FDEs were employed to model financial problems. [13][14][15] It should be noted that the classical Black-Scholes (BS) model 16,17 was derived by imposing quite restrictive assumptions, for example, stock pays no dividend, interest rates are constant, transaction costs are eliminated and the values of short-term rates are available.…”

Lyapunov stability and wave analysis of Covid-19 omicron variant of real data with fractional operator

“…We will look at the stability and existence of Hopf bifurcation in fractional-order complex-valued neural networks in [4] , [5] , [6] . Investigate the asymptotic behaviour of immunogenic tumour dynamics using a new fractional model built using the general fractional operators approach [7] , [33] , [34] . Using another fractional order derivative constructed as a kernel based on the generalized MITTAG–LEFFLER function, the predatory model is generated in [35] , [36] , [37] .…”

Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal

“…In particular, mathematical modelling plays an important role in the prediction of possible scenarios and in its effective control [2,3]. Readers interested in fractional modelling are referred to [4,5] and references therein.…”