Cauchy problem for the fractal diffusion equation with argument deviation

Drin  Svitlana Serhiyivna; Drin  Yaroslav Mykhailovych

Drin Svitlana Serhiyivna ¹ , Drin Yaroslav Mykhailovych ²

¹ Department of Mathematics, National University "Kyiv-Mohyla Academy" , Kyiv, 04655, Ukraine

² Department of Mathematical Problems of Management and Cybernetics, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: Cauchy problem, the fractal diffusion equation with argument deviation

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Abstract

We prove the solvability of the Cauchy problem for a quasilinear pseudodifferential equation with fractal derivative with respect to time $t$ of order $α ∈ (0,1)$ second derivative with respect to spatial argument $x$ and deviation time variable using the step by step method.

References

[1] Kochubey A.N. Diffusion of fractional order // Differential Equations, 1990. 26, No 4. P. 485-492.

[2] Kochubey A.N., Eidelman S.D. Equations of one-dimensional fractal diffusion // Dokl. of NAS of Ukraine. 2003, No 12. P. 11-16.

[3] Eidelman S.D., Ivasyshen S.D., Kochubei A.N. Analytic methods in the theory of differential and pseudo-differential equations of parabolic type. - Basel-Boston-Berlin: Birkhäuser Verlag, 2004. - 390 p.

[4] Matiychuk M.I. Parabolic and elliptic problems in Dini spaces: a monograph. - Chernivtsi, 2010. - 248 p.

[5] Drin S.S., Drin Y.M. Cauchy problem for the model equation of fractal diffusion // International scientific conference “Modern problems of mathematical modeling and computational methods”, February 19-22, 2015 (Rivne, 2015). - P. 74.

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ACS Style: Drin , S.S.; Drin , Y.M. Cauchy problem for the fractal diffusion equation with argument deviation. Bukovinian Mathematical Journal. 2016, 3
AMA Style: Drin SS, Drin YM. Cauchy problem for the fractal diffusion equation with argument deviation. Bukovinian Mathematical Journal. 2016; 3(2).
Chicago/Turabian Style: Svitlana Serhiyivna Drin , Yaroslav Mykhailovych Drin . 2016. "Cauchy problem for the fractal diffusion equation with argument deviation". Bukovinian Mathematical Journal. 3 no. 2.

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