Generalized Monotone Method for System of Riemann-Liouville Fractional Reaction-Diffusion Equations

Document Type : Original Article


Department of PG Studies and Research in Mathematics, Shrikrishana Mahavidyalaya, Gunjoti, Dist.Osmanabad-413606, India


In this paper, our aim is to obtain the integral representation for the solution of linear Riemann-Liouville reaction-diffusion equations of order $q$ in terms of Green's function where $ 0<q<1 .$ We have developed a generalized monotone method for non-linear weakly coupled system of Riemann-Liouville reaction-diffusion equations when the forcing term is the sum of increasing and decreasing functions. The generalized monotone method yields monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. Under uniqueness assumption, we proved the existence of a unique solution for the non-linear system of Riemann-Liouville reaction-diffusion equations.


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