Modern Fractional Differential Equations
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Beschreibung
Inspired by an abundance of existing flaws in the literature on fractional differential equations, this book serves an important purpose by providing a meticulous presentation with new insights. Placing the topics on a firm theoretical foundation, it is designed for researchers and students who already have a base of understanding to build on. It is a solid reference which may also be used as either a supplementary or a primary text in a course in fractional calculus.
The book provides precise and correct versions of the following topics: Riemann-Liouville (R-L) fractional integrals; R-L type fractional derivatives and Caputo fractional derivatives; equivalences of linear or nonlinear first order or higher order R-L type or Caputo FDEs; Abel type R-L integral equations; the identities of the R-L fractional integrals composed with the corresponding R-L type or Caputo fractional derivatives. The exposition is mostly self-contained. For the few classical theorems whose proofs are not provided, it is clearly noted where proofs may be found.
Inspired by an abundance of existing flaws in the literature on fractional differential equations, this book serves an important purpose by providing a meticulous presentation with new insights. Placing the topics on a firm theoretical foundation, it is designed for researchers and students who already have a base of understanding to build on. It is a solid reference which may also be used as either a supplementary or a primary text in a course in fractional calculus.
The book provides precise and correct versions of the following topics: Riemann-Liouville (R-L) fractional integrals; R-L type fractional derivatives and Caputo fractional derivatives; equivalences of linear or nonlinear first order or higher order R-L type or Caputo FDEs; Abel type R-L integral equations; the identities of the R-L fractional integrals composed with the corresponding R-L type or Caputo fractional derivatives. The exposition is mostly self-contained. For the few classical theorems whose proofs are not provided, it is clearly noted where proofs may be found.
Provide precise definitions of fractional derivatives and correct results on equivalences of FDEs Provide new results on the existence and uniqueness of solutions and local solutions for nonlinear first order FDEs Provide latest development of fractional integrals, derivatives and differential equations (FDEs)
Autor*in
Kunquan Lan
Themen in »Modern Fractional Differential Equations«
Riemann-Liouville type fractional derivatives Caputo fractional derivatives Equivalences of first order fractional differential equations Equivalences of higher order fractional differential equations Abel type integral equations Initial value problems of fractional differential equations Fixed point theorems Generalized Riemann-Liouville fractional integrals