We use the block pulse functions (BPFs) and their operational matrix to approximate solution of a system of multi-term fractional mixed Volterra-Fredholm integro-differential equations. Firstly, we homogenize it and then convert it to the system of algebraic equations. By solving the system of algebraic equations, a numerical solution is obtained.After demonstrating the method's convergence, several examples are presented. Comparing the results confirms the proposed method's applicability, accuracy, and efficiency.

Abstract:One of the most important biochemical reactions is catalyzed by enzymes. A numerical method to solve nonlinear equations of enzyme kinetics, known as the Michaelis and Menten equations, together with fuzzy initial values is introduced. The numerical method is based on the fourth order Runge-Kutta method, which is generalized for a fuzzy system of differential equations. The convergence and stability of the method are also presented. The capability of the method in fuzzy enzyme kinetics is demonstrated by some numerical examples.

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