In the present paper, we establish some compositions formulas for Marichev-Saigo-Maeda (MSM) fractional calculus operators with k-Struve function S_{\nu ,c}^k as of the kernel. The results are presented in terms of generalized k-Wright function _p\Psi _q^k .

The aim of this paper is to develop a fractional order mathematical model for describing the dispersal of Hepatitis B virus (HBV). We also provide a rigorous mathematical analysis of the stability of the disease-free balance and the endemic balance of the system based on the number of computed reproductions. Here the infectious disease HBV model is described mathematically in a nonlinear system of differential equations in a caputo sense, and hence Jacobi collocation method is used to reduce into a system of nonlinear equations. Finally, Newton Raphson method is used for the systems of nonlinear equations to arrive at an approximate solution and MATLAB 2018 has helped us to simulate the nature of each compartment and effects of the possible control strategies (i.e., vaccination and isolation).

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