Cauchy type problems for fractional differential equations

Karimov E. Ruzhansky M. Tokmagambetov N.
2022 Taylor and Francis Ltd.

Integral Transforms and Special Functions
2022 #33 Issue 1 47 - 64 pp.

While it is known that one can consider the Cauchy problem for evolution equations with Caputo derivatives, the situation for the initial value problems for the Riemann–Liouville derivatives is less understood. In this paper, we propose new type initial, inner, and inner-boundary value problems for fractional differential equations with the Riemann–Liouville derivatives. The results on the existence and uniqueness are proved, and conditions on the solvability are found. The well-posedness of the new type of initial, inner, and inner-boundary conditions is also discussed. Moreover, we give explicit formulas for the solutions. As an application fractional partial differential equations for general positive operators are studied.

Cauchy type problem , inner problem , inner-boundary problem , Wave equation , well-posedness

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V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

V.I.Romanovskiy Institute of Mathematics
Department of Mathematics: Analysis
School of Mathematical Sciences
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026