Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order

• Autorzy: Małgorzata Klimek , Marek Błasik
• Języki publikacji: EN

Abstrakty

EN

Two-term semi-linear and two-term nonlinear fractional differential equations (FDEs) with sequential Caputo derivatives are considered. A unique continuous solution is derived using the equivalent norms/metrics method and the Banach theorem on a fixed point. Both, the unique general solution connected to the stationary function of the highest order derivative and the unique particular solution generated by the initial value problem, are explicitly constructed and proven to exist in an arbitrary interval, provided the nonlinear terms fulfil the corresponding Lipschitz condition. The existence-uniqueness results are given for an arbitrary order of the FDE and an arbitrary partition of orders between the components of sequential derivatives.

Słowa kluczowe

EN

Fractional derivative; Fractional differential equation; Fixed point condition; Equivalent norms/metrics; Initial value problem

Kategorie tematyczne

• 45Jxx: Integro-ordinary differential equations
• 26A33: Fractional derivatives and integrals
• 34A08: Fractional differential equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 1981-1994

Daty

wydano

2012-12-01

online

2012-10-12

Twórcy

autor

Małgorzata Klimek

• Institute of Mathematics, Częstochowa University of Technology, Dąbrowskiego 73, 42-200, Częstochowa, Poland

autor

Marek Błasik

• Institute of Mathematics, Częstochowa University of Technology, Dąbrowskiego 73, 42-200, Częstochowa, Poland

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0112-9