Monotone iterative technique for fractional differential equations with periodic boundary conditions

• Autorzy: Ramirez J. D. , Vatsala A. S.
• Języki publikacji: EN

Abstrakty

EN

In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.

Słowa kluczowe

EN

Riemann-Liouville fractional derivative; monotone method; periodic boundary value problem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2009
• Tom: Vol. 29, no. 3
• Strony: 289--304
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Ramirez J. D.

autor

Vatsala A. S.

• University of Louisiana Lafayette Department of Mathematics Lafayette, LA 70504 USA,

Bibliografia

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• [4] V. Lakshmikantham, S. Leela, D. Vasundhara, Theory of fractional dynamic systems, Cambridge Scientific Publishers, 2009.
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• [6] V. Lakshmikantham, A. Vatsala, Basic theory of fractional differential equations, Non-linear Analysis TMAA 69 (2008), 3837-3343.
• [7] V. Lakshmikantham, A. Vatsala, General uniqueness and monotone iterative technique for fractional differential equations, Applied Mathematics Letter 21 (2008), 828-834.
• [8] B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York-London, 1974.
• [9] C. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, 1992.
• [10] I. Podlubny, Fractional Di_erential Equations, Academic Press, San Diego, 1999.