Monotone iterative technique for finite systems of nonlinear Riemann-,Lliouville fractional differential equations

• Autorzy: Denton Z. , Vatsala A.S.
• Języki publikacji: EN

Abstrakty

EN

Comparison results of the nonlinear scalar Riemann-Liouville fractional differential equation of order q, 0 < q ≤ 1, are presented without requiring Hölder continuity assumption. Monotone method is developed for finite systems of fractional differential equations of order q, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional differential system is proved.

Słowa kluczowe

EN

fractional differential systems; coupled lower and upper solutions; mixed quasimonotone property

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 3
• Strony: 327--339
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Denton Z.

autor

Vatsala A.S.

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

Bibliografia

• [1] Z. Denton, A. Vatsala, Fractional integral inequalities and applications, Comput. Math. Appl. 59 (2010), 1087–1094.
• [2] A. Kilbas, H. Srivastava, J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, North Holland, 2006.
• [3] G. Ladde, V. Lakshmikantham, A. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman Publishing Inc., 1985.
• [4] V. Lakshmikantham, S. Leela, D. Vasundhara, Theory of fractional dynamic systems, Cambridge Scientific Publishers, 2009.
• [5] B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York – London, 2002.
• [6] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
• [7] J.D. Ramírez, A.S. Vatsala, Monotone iterative technique for fractional differential equations with periodic boundary conditions, Opuscula Math. 29 (2009) 3, 289–304.