We study the fractional diffusion equation with changing direction of evolution. We consider the boundary value problem for this equation and prove the existence of a generalized solution.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Gripenberg, S.-O. Londen, and O. Staffans, Volterra Integral and Functional Equations, Cambridge Univ. Press, Cambridge (1990).
R. Zacher “Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients,” J. Math. Anal. Appl. 348, No. 1, 137–149 (2008).
Karel Van Bockstal, “Existence of a unique weak solution to a non-autonomous time-fractional diffusion equation with space-dependent variable order,”, Adv. Difference Equ. 2021, Article ID 314 (2021). DOI: https://doi.org/10.1186/s13662-021-03468-9
R. Zacher, “Weak solutions of abstract evolutionary integro-differential equations in Hilbert Spaces,” Funkc. Ekvacioj, Ser. Int. 52, No. 1, 1–18 (2009).
R. Zacher, “A weak Harnack inequality for fractional evolution equations with discontinuous coefficients,” Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 12, No. 4, 903–940 (2013).
A. N. Artyushin “Fractional integral inequalities and their applications to degenerate differential equations with the Caputo fractional derivative,” Sib. Math. J. 61, No. 2, 208–221 (2020).
S. G. Pyatkov, “Boundary value problems for some classes of singular parabolic equations,” Sib. Adv. Math. 14, No. 3, 63–125 (2004).
V. E. Fedorov and M. M. Turov, “The defect of a Cauchy type problem for linear equations with several Tiemann–Liouville derivatives,” Sib. Math. J. 62, No. 5, 925–942 (2021).
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, New York, NY (1993).
A. N. Artyushin, “A boundary value problem for a mixed type equation in a cylindrical domain,” Sib. Math. J. 60, No. 2, 209–222 (2019).
Author information
Authors and Affiliations
Corresponding author
Additional information
International Mathematical Schools. Vol. 6. Mathematical Schools in Uzbekistan
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Artyushin, A., Dzhamalov, S. Differential Equations with Fractional Derivatives and Changing Direction of Evolution. J Math Sci 277, 366–375 (2023). https://doi.org/10.1007/s10958-023-06841-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06841-z