Basic theory of fractional differential equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 8, 2008, Pages 2677-2682

  Lakshmikantham, V ^a   Vatsala, A S ^b  

^a Florida Institute of Technology   (United States)

^b UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

Author keywords

Basic theory of existence; Comparison result; Fractional differential equations

Indexed keywords

INITIAL VALUE PROBLEMS; MATHEMATICAL OPERATORS;

BASIC THEORY; CLASSICAL APPROACH; COMPARISON RESULT; DIFFERENTIAL OPERATORS; EXTREMAL SOLUTIONS; FRACTIONAL DIFFERENTIAL EQUATIONS; GLOBAL EXISTENCE OF SOLUTIONS; LOCAL EXISTENCE;

DIFFERENTIAL EQUATIONS;

EID: 53949111458     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.08.042     Document Type: Article

References (10)

1. M. Caputo, Linear models of dissipation whose Q is almost independent, II, Geophy. J. Roy. Astronom. 13 (1967) 529-539.
2. W.G. Gl̈ockle, T.F. Nonnenmacher, A fractional calculus approach to self similar protein dynamics, Biophys. J. 68 (1995) 46-53.
3. K. Diethelm, N.J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl. 265 (2002) 229-248.
4. K. Diethelm, N.J. Ford, Multi-order fractional differential equations and their numerical solution, Appl. Math. Comput. 154 (2004) 621-640.
5. K. Diethelm, A.D. Freed, On the solution of nonlinear fractional differential equations used in the modeling of viscoplasticity, in: F. Keil, W. Mackens, H. Vob, J. Werther (Eds.), Scientific Computing in Chemical Engineering II: Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties, Springer, Heidelberg, 1999, pp. 217-224.
6. V. Kiryakova, Generalized fractional calculus and applications, in: Pitman Res. Notes Math. Ser., vol. 301, Longman-Wiley, New York, 1994.
7. V. Lakshmikantham, S. Leela, Differential and Integral Inequalities, vol. I, Academic Press, New York, 1969.
8. R. Metzler, W. Schick, H.G. Kilian, T.F. Nonnenmacher, Relaxation in filled polymers: A fractional calculus approach, J. Chem. Phys. 103 (1995) 7180-7186.
9. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
10. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.