Sequential fractional differential equations with hadamard derivative

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 12, 2011, Pages 4689-4697

  Klimek, M ^a  

^a CZESTOCHOWA UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Banach theorem; Equivalent metrics; Existence and uniqueness of solutions; Fox functions series; Fractional differential equation; Hadamard derivative

Indexed keywords

DIFFERENTIAL EQUATIONS;

BANACH THEOREM; EQUIVALENT METRIC; EXISTENCE AND UNIQUENESS OF SOLUTION; FOX FUNCTION SERIES; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL OPERATORS; HADAMARD; HADAMARD DERIVATIVE; NON-HOMOGENEOUS TERMS; SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 79960285223     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.01.018     Document Type: Article

References (19)

1. Lakshmikantham V., Leela S., Vasundhara Devi J. Theory of Fractional Dynamic Systems 2009, Cambridge Scientific Publishers, Cambridge.
2. Podlubny I. Fractional Differential Equations 1999, Academic Press, San Diego.
3. Miller K.S., Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations 1993, Wiley and Sons, New York.
4. Kilbas A.A., Srivastawa H.M., Trujillo J.J. Theory and Applications of Fractional Differential Equations 2006, Elsevier, Amsterdam.
5. Kiryakova V. Generalized Fractional Calculus and Applications 1994, Longman-Wiley, New York.
6. Kilbas A.A., Trujillo J.J. Differential equation of fractional order: methods, results and problems. I. Appl Anal 2001, 78:153-192.
7. Kilbas A.A., Trujillo J.J. Differential equation of fractional order: methods, results and problems. II. Appl Anal 2002, 81:435-493.
8. Magin R. Fractional Calculus in Bioengineering 2006, Begell House Publisher, Redding.
9. West B.J., Bologna M., Grigolini P. Physics of Fractional Operators 2003, Springer-Verlag, Berlin.
10. Michalski MW. Derivatives of noninteger order and their applications. Mathematicae CCCXXVIII, Institute of Mathematics 1993, Polish Academy of Science, Warsaw.
11. Klimek M. On Solutions of Linear Fractional Differential Equations of a Variational Type 2009, The Publishing Office of the Czestochowa University of Technology, Czestochowa.
12. Kilbas A.A., Rivero M., Rodriguez-Germá L., Trujillo J.J. α-Analytic solutions of some linear fractional differential equations with variable coefficients. Appl Math Comput 2007, 187:239-249.
13. Rivero M., Rodriguez-Germá L., Trujillo J.J. Linear fractional differential equations with variable coefficients. Appl Math Lett 2008, 21:892-897.
14. Wei Zhongli, Li Qingdong, Che Junling Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative. J Math Anal Appl 2010, 367:260-272.
15. Kilbas A.A., Saigo M. H-Transforms. Theory and Applications 2004, Chapman & Hall/CRC, Boca Raton.
16. Bielecki A. Une remarque sur la methode de Banach-Cacciopoli-Tikhonov dans la theorie des equations differentielles ordinaires. Bull Acad Polon Sci Cl 1956, III-IV:261-264.
17. Baleanu D., Mustafa O.G. On the global existence of solutions to a class of fractional differential equations. Comput Math Appl 2010, 59:1835-1841.
18. El-Raheem Z.F.A. Modification of the application of a contraction mapping method on a class of fractional differential equation. Appl Math Comput 2003, 137:371-374.
19. Lakshmikantham V., Vasundhara Devi J. Theory of fractional differential equations in a Banach space. Eur J Pure Appl Math 2008, 1:38-45.