In this study, using the Holling type II response function and prey refuge, we bring fractional order into an eco-epidemiological paradigm with diseased prey in which the predator consumes a vast amount of healthy prey in an excessively disproportionately large amount. We show that there are solutions to the fractional order eco-epidemiological paradigm and that these solutions are distinct, non-negativity, and limited. Additionally, we generated a number of equilibrium points and investigated the local and global stability of the interior equilibrium point. We explore the roles that fractional order and the prey shelter play in maintaining the stability of the proposed system’s equilibrium point. Numerous examples are used to illustrate the results, and numerical simulations are used to support our theoretical conclusions.
A second order linearly independent solution of the fractional Bessel equation is defined by utilizing the Wronskian matrix and the fractional Bessel function of the first kind of complex order. Additionally, as an application, a precise solution to a reformulated fractional type heat equation in one and two dimensions in a circular plate is produced.
Within the definition of the local fractional derivative, we present a reliable and effective method for solving the Lane- Emden and Emden-Fowler models in the current article. Numerous fields of research and engineering can benefit from the use of these models. The proposed technique is named the local fractional homotopy analysis method. The method is applied for both models of k order and tested for several examples. This method proves to be effective in handling such models when compared to other similar models. The results indicate the robustness of the technique and the possibility of its application to other models in the future.
In this study, a conformable double Sumudu-Elzaki (CDSE) transformation and a decomposition method are combined to develop a new method that solves nonlinear problems considering some specific conditions. This combination can be referred to as the CDSE-Decomposition method. Furthermore, we explain and discuss the main features and main results of the presented method. The CDSE-Decomposition method presents analytic series solutions with high convergence to the exact solution in a closed form. The benefit of utilizing the proposed technique is that it presents analytic series solutions to the objective equations without the requirement for any constrained assumptions, transformation or discretization. In addition, various numerical experiments are presented to prove the efficiency of the obtained method. The results show the power and effectiveness of the proposed approach in handling a range of physical and engineering problems that arize in mathematics.
In this paper, we have introduced a mathematical model of virotherapy for medication of tumor cells by using fractional calculus. In the current model four differential conditions are presented which portray cooperation among non-infected tumor cells, infected tumor cells, virions and effector T cells. We will examine the presence and uniqueness of the introduced mathematical model. We will likewise concentrate on the local stability of equilibrium points. Then, we will discuss the numerical solutions to investigate the use of fractional order derivative and different variables. We will likewise plot a few charts to show the outcomes.
