Representation of solution for fully nonlocal diffusion equations with deviation time variable

I. I. Drin; S. S. Drin; Ya. M. Drin

doi:10.1117/12.2304312

18 January 2018 Representation of solution for fully nonlocal diffusion equations with deviation time variable

I. I. Drin, S. S. Drin, Ya. M. Drin

Proceedings Volume 10612, Thirteenth International Conference on Correlation Optics; 106120E (2018) https://doi.org/10.1117/12.2304312
Event: Thirteenth International Conference on Correlation Optics, 2017, Chernivtsi, Ukraine

Abstract

We prove the solvability of the Cauchy problem for a nonlocal heat equation which is of fractional order both in space and time. The representation formula for classical solutions for time- and space- fractional partial differential operator D^a_t + a² (-Δ) ^γ/2 (0 ≤ α ≤ 1, γ ε (0, 2]) and deviation time variable is given in terms of the Fox H-function, using the step by step method.

Citation Download Citation

I. I. Drin, S. S. Drin, and Ya. M. Drin "Representation of solution for fully nonlocal diffusion equations with deviation time variable", Proc. SPIE 10612, Thirteenth International Conference on Correlation Optics, 106120E (18 January 2018); https://doi.org/10.1117/12.2304312

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