THE ROTHE METHOD FOR SOLVING A NONLINEAR DIFFUSION SYSTEM WITH MULTI-TERM FRACTIONAL INTEGRAL OPERATORS AND NONLINEAR COUPLING TERMS

Jinsheng Du (), Lijie Li and Nguyen van Thien ()
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Jinsheng Du: College of Mathematics and Information Science, Guangxi University, Nanning 530004, P. R. China
Lijie Li: ��Guangxi Colleges and Universities Key Laboratory of Complex System, Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, P. R. China
Nguyen van Thien: ��Department of Mathematics, FPT University, Education Zone, Hoa Lac High Tech Park, Km29 Thang Long Highway, Thach That Ward, Hanoi, Vietnam

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-18

Abstract: 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.

Keywords: Accretive Operator; Strong Solution; Fractional Integral Diffusion Equation; Coupled System; Rothe’s Method; Fractional (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401127

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