Initial value problem for a fractional order equation with the Gerasimov–Caputo derivative with involution
L.M. Eneeva
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Abstract. The paper considers a linear ordinary differential equation with a fractional derivative in the Gerasimov–Caputo sense. The equation under consideration belongs to the class of differential equations that arise, in particular, in the study of boundary value problems for differential equations containing a composition of left- and right-hand derivatives of fractional order, which, in turn, serve as the basis for modeling various physical and geophysical processes. In particular, such equations arise when describing dissipative oscillatory systems. In this work, the initial value problem in the unit interval is studied for the equation under consideration. A theorem for the existence and uniqueness of a solution to the problem under study is proven, and an explicit representation of the solution is constructed.
Keywords: fractional order equation, Cauchy problem, Gerasimov–Caputo derivative, involution, fundamental solution
For citation. Eneeva L.M. Initial value problem for a fractional order equation with the Gerasimov–Caputo derivative with involution. News of the Kabardino-Balkarian Scientific Center of RAS. 2024. Vol. 26. No. 6. Pp. 19–25. DOI: 10.35330/1991-6639-2024-26-6-19-25
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Information about the author
Liana M. Eneeva, Candidate of Physical and Mathematical Sciences, Senior Researcher of Department of
Mathematical Modeling of Geophysical Processes at the Institute of Applied Mathematics and Automation of
the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
360000, Russia, Nalchik, 89 A Shortanov street;
Eneeva72@list.ru, ORCID: https://orcid.org/0000-0003-2530-5022, SPIN-code: 3403-8412