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

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.

### 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
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### References:

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