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Abadias, Luciano; Alvarez, Edgardo; Díaz, Stiven

Subordination principle, Wright functions and large-time behavior for the discrete in time fractional diffusion equation. (English) Zbl 1478.35029

J. Math. Anal. Appl. 507, No. 1, Article ID 125741, 23 p. (2022).
Summary: The main goal in this paper is to study asymptotic behavior in \(L^p( \mathbb{R}^N)\) for the solutions of the fractional version of the discrete in time \(N\)-dimensional diffusion equation, which involves the Caputo fractional \(h\)-difference operator. The techniques to prove the results are based in new subordination formulas involving the discrete in time Gaussian kernel, and which are defined via an analogue in discrete time setting of the scaled Wright functions. Moreover, we get an equivalent representation of that subordination formula by Fox H-functions.

Cited in 1 Document

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35R11 Fractional partial differential equations
35K15 Initial value problems for second-order parabolic equations
39A12 Discrete version of topics in analysis

Keywords:

subordination formula; scaled Wright function; fractional difference equations; large-time behavior; decay of solutions; discrete fundamental solution
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\textit{L. Abadias} et al., J. Math. Anal. Appl. 507, No. 1, Article ID 125741, 23 p. (2022; Zbl 1478.35029)
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