The Rothe Method For Solving A Nonlinear Diffusion System With Multi-Term Fractional Integral Operators And Nonlinear Coupling Terms

In this work, we explore a new class of diffusion systems involving multi-term fractional integral operators and nonlinear coupling terms in a Hilbert space. First, we use a time semi-discrete approach grounded in the backward Euler difference formulation (i.e. Rothe’s method) to introduce a discrete iterative system. Then, the existence and uniqueness as well as the priori estimations of solution for the discrete iterative system are proved. Moreover, an approximating parabolic coupled system is considered, and an convergence result which shows that the solution of approximating coupled system converges to the unique strong solution of original problem, is obtained. Finally, we give three examples to illustrate the validity of the theoretical results.