Fractional Calculus and Time-Fractional Differential Equations: Revisit and Construction of a Theory

For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the Riemann-Liouville derivatives within Sobolev spaces of fractional orders, including negative ones. Our approach enables a unified treatment for fractional calculus and time-fractional differential equations. We formulate initial value problems for fractional ordinary differential equations and initial boundary value problems for fractional partial differential equations to prove well-posedness and other properties. © 2022 by the author. Licensee MDPI, Basel, Switzerland.

Authors
Yamamoto M. 1, 2, 3, 4
Journal
Publisher
MDPI AG
Number of issue
5
Language
English
Status
Published
Number
698
Volume
10
Year
2022
Organizations
  • 1 Graduate School of Mathematical Sciences, The University of Tokyo, Komaba Meguro, Tokyo, 153-8914, Japan
  • 2 Academy of Romanian Scientists, Ilfov, nr. 3, Bucuresti, 062217, Romania
  • 3 Accademia Peloritana dei Pericolanti, Palazzo Università, Piazza S. Pugliatti 1, Messina, 98122, Italy
  • 4 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
Keywords
Fractional calculus; Fractional Sobolev spaces; Operator theory; Time-fractional differential equations
Date of creation
06.07.2022
Date of change
06.07.2022
Short link
https://repository.rudn.ru/en/records/article/record/83784/
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