On the global existence of solutions to a class of fractional differential equations

Computers and Mathematics with Applications

Volumn 59, Issue 5, 2010, Pages 1835-1841

  Bǎleanu, Dumitru ^a,b   Mustafa, Octavian G ^a  

^a CANKAYA UNIVERSITY   (Turkey)

^b INSTITUTE OF SPACE SCIENCES   (Romania)

Author keywords

Fixed point theory; Fractional differential equation; Global existence of solution

Indexed keywords

BASIC THEORY; FIXED POINT THEORY; FRACTIONAL DIFFERENTIAL EQUATIONS; GLOBAL EXISTENCE; GLOBAL EXISTENCE OF SOLUTIONS; LARGE CLASS;

DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEMS;

NONLINEAR EQUATIONS;

EID: 76649111047     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.08.028     Document Type: Article

References (39)

1. Oldham K.B., and Spanier J. The Fractional Calculus (1974), Academic Press, New York
2. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional integrals and derivatives. Theory and Applications (1993), Gordon and Breach, Switzerland
3. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego
4. Diethelm K., and Ford N.J. Analysis of fractional differential equations. J. Math. Anal. Appl. 265 (2002) 229-248
5. Caputo M. Linear models of dissipation whose Q is almost frequency indepedent II. Geophys. J. Roy. Astron. 13 (1967) 529-539
6. Schneider W.R., and Wyss W. Fractional diffusion and wave equations. J. Math. Phys. 30 (1989) 134-144
7. Glöcke W.G., and Nonnenmacher T.F. Fractional integral operators and Fox functions in the theory of viscoelasticity. Macromolecules 24 (1991) 6426-6434
8. Zaslavsky G.M. Hamiltonian Chaos and Fractional Dynamics (2005), Oxford University Press, Oxford
9. Kilbas A.A., Srivastava H.M., and Trujillo J.J. Theory and Applications of Fractional Differential Equations (2006), Elsevier, Netherlands
10. Magin R.L. Fractional Calculus in Bioengineering (2006), Begell House Publ., Inc., Connecticut
11. Mainardi F., Luchko Yu., and Pagnini G. Fract. Calc. Appl. Anal. 4 (2001) 153-161
12. Tenreiro Machado J.A. A probabilistic interpretation of the fractional-order differentiation. Fract. Calc. Appl. Anal. 8 (2003) 73-80
13. Magin R.L., Abdullah O., Bǎleanu D., and Xiaohong J.Z. Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation. J. Magn. Reson. 190 (2008) 255-270
14. Ahlfors L.V. Complex analysis. An Introduction to the Theory of Analytic Functions of One Complex Variable (1979), McGraw-Hill, New York
15. Glöcke W.G., and Nonnenmacher T.F. A fractional calculus approach to self-similar protein dynamics. Biophys. J. 68 (1995) 46-53
16. Metzler R., Schick W., Kilian H.G., and Nonennmacher T.F. Relaxation in filled polymers: A fractional calculus approach. J. Chem. Phys 103 (1995) 7180-7186
17. Advances in fractional calculus. In: Sabatier J., Agrawal O.P., and Tenreiro Machado J.A. (Eds). Theoretical Developments and Applications in Physics and Engineering (2007), Springer-Verlag, Dordrecht
18. Agrawal O.P. Formulation of Euler-Lagrange equations for fractional variational problems. J.Math. Anal. Appl. 272 (2002) 368-379
19. Atanackoviç T.M., Konjik S., and Pipiloviç S. Variational problems with fractional derivatives: Euler-Lagrange equations. J. Phys. A: Math. Theor. 41 9 (2008) art. no. 095201
20. Bǎleanu D., Muslih S.I., and Taş K. Fractional Hamiltonian analysis of higher order derivatives systems. J. Math. Phys. 47 (2006) art. no. 103503
21. Bǎleanu D., and Agrawal O.P. Fractional Hamilton formalism within Caputo's derivative. Czech. J. Phys. 56 (2006) 1087-1092
22. Bǎleanu D., and Muslih S.I. Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives. Phys. Scr. 72 (2005) 119-121
23. Bǎleanu D., and Avkar T. Lagrangians with linear velocities within Riemann-Liouville fractional derivatives. Nuovo Cim. B 119 (2004) 73-79
24. Bǎleanu D., Muslih S.I., and Rabei E.M. On fractional Euler-Lagrange and Hamilton equations and the fractional generalization of total time derivative. Nonlinear Dynam. 53 (2008) 67-74
25. Bǎleanu D., and Trujillo J.J. New applications of fractional variational principles. Rep. Math. Phys. 61 (2008) 331-335
26. Bǎleanu D. On exact solutions of a class of fractional Euler-Lagrange equations. Nonlinear Dynam. 52 (2008) 199-206
27. Frederico G.S.F., and Torres D.F.M. A formulation of Noether's theorem for fractional problems of the calculus of variations. J. Math. Anal. Appl. 334 (2007) 834-846
28. Klimek M. Fractional sequential mechanics-models with symmetric fractional derivative. Czech. J. Phys. 51 (2001) 1348-1356
29. Klimek M. Lagrangean and Hamiltonian fractional sequential mechanics. Czech. J. Phys. 52 (2002) 1247-1252
30. Muslih S.I., and Bǎleanu D. Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives. J. Math. Anal. Appl. 304 (2005) 599-606
31. Lakshmikantham V., and Vatsala A.S. Basic theory of fractional differential equations. Nonlinear Anal. TMA 69 (2008) 2677-2682
32. Lakshmikantham V. Theory of fractional functional differential equations. Nonlinear Anal. TMA 69 10 (2008) 3337-3343 10.1016/j.na.2007.09.025
33. Hartman P. Ordinary Differential Equations (1964), Wiley & Sons, New York
34. Weissinger J. Zur Theorie und Anwendung des Iterationsverfahrens. Math. Nachr. 8 (1952) 193-212
35. Erdélyi A., Magnus W., Oberhettinger F., and Tricomi F.G. Higher Transcendental Functions III (1955), McGraw-Hill, New York
36. El-Raheem Z.F.A. Modification of the application of a contraction mapping method on a class of fractional differential equation. Appl. Math. Comput. 137 (2003) 371-374
37. Kartsatos A.G. Advanced Ordinary Differential Equations (1980), Mariner Publ., Tampa, Florida
38. Brezis H. Analyse fonctionelle. Théorie et applications (1999), Dunod, Paris
39. Dugundji J., and Granas A. Fixed Point Theory I (1982), Sci. Publ., Warszawa