Opial type inequalities involving Riemann-Liouville fractional derivatives of two functions with applications

Mathematical and Computer Modelling

Volumn 48, Issue 3-4, 2008, Pages 344-374

  Anastassiou, George A ^a  

^a University of Memphis   (United States)

Author keywords

Opial type inequality; Riemann Liouville fractional derivative; System of fractional differential equations; Uniqueness of solution; Upper bound of solution

Indexed keywords

(MIN ,MAX ,+) FUNCTIONS; GENERAL (CO); RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES;

EID: 44849121375     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2007.09.017     Document Type: Article

References (17)

1. Agarwal R.P. Sharp Opial-type inequalities involving r-derivatives and their applications. Tôhoku Math. J. 47 (1995) 567-593
2. Agarwal R.P., and Pang P.Y.H. Sharp Opial-type inequalities involving higher order derivatives of two functions. Math. Nachr. 174 (1995) 5-20
3. Agarwal R.P., and Pang P.Y.H. Opial Inequalities with Applications in Differential and Difference Equations (1995), Kluwer Academic Publishers, Dordrecht, Boston, London
4. Aliprantis C.D., and Burkinshaw O. Principles of Real Analysis. third ed. (1998), Academic Press, San Diego, CA
5. Anastassiou G.A. General fractional Opial type inequalities. Acta Appl. Math. 54 (1998) 303-317
6. Anastassiou G.A. Opial type inequalities involving fractional derivatives of functions. Nonlinear Stud. 6 2 (1999) 207-230
7. Anastassiou G.A., and Goldstein J.A. Fractional Opial type inequalities and fractional differential equations. Result. Math. 41 (2002) 197-212
8. Anastassiou G.A., Koliha J.J., and Pecaric J. Opial inequalities for fractional derivatives. Dynam. Systems Appl. 10 3 (2001) 395-406
9. p-inequalities for fractional derivatives. Int. J. Math. Math. Sci. 31 2 (2002) 85-95
10. Handley G.D., Koliha J.J., and Pecaric J. Hilbert-Pachpatte type integral inequalities for fractional derivatives. Fract. Calc. Appl. Anal. 4 1 (2001) 37-46
11. In: Hilfer R. (Ed). Applications of Fractional Calculus in Physics (2000), Volume published by World Scientific, Singapore
12. Kiryakova V. Generalized Fractional Calculus and Applications. Pitman Research Notes in Math. Series vol. 301 (1994), Longman Scientific and Technical, Harlow; copublished in U.S.A with John Wiley & Sons, Inc., New York
13. Miller K., and Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), John Wiley & Sons, Inc., New York
14. Oldham K., and Spanier J. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (2006), Dover Publications, New York
15. Opial Z. Sur une inégalite. Ann. Polon. Math. 8 (1960) 29-32
16. Podlubny I. Fractional Diferential Equations (1999), Academic Press, San Diego
17. Whittaker E.T., and Watson G.N. A Course in Modern Analysis (1927), Cambridge University Press