Existence of fractional integral equation with hysteresis

Applied Mathematics and Computation

Volumn 176, Issue 2, 2006, Pages 684-687

  Darwish, Mohamed Abdalla ^a   El Bary, A A ^b  

^a Alexandria University   (Egypt)

^b Egypt Mansoura University   (Egypt)

Author keywords

Fractional integral; Hysteresis; Schauder's fixed point theorem

Indexed keywords

HYSTERESIS; MATHEMATICAL MODELS; THEOREM PROVING;

FRACTIONAL INTEGRAL; SCHAUDER'S FIXED POINT THEOREM;

INTEGRAL EQUATIONS;

EID: 33646481618     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.10.014     Document Type: Article

References (17)

1. Brokate M., and Sprekels J. Hysteresis and phase transitions. Appl. Math. Sci. 121 (1996), Springer-Verlag, New York
2. Darwish M.A. On nonlinear Fredholm-Volterra integral equations with hysteresis. Appl. Math. Comput. 156 1 (2004) 479-484
3. Darwish M.A. On solvability of Urysohn-Volterra equations with hysteresis in weighted spaces. J. Integral Equat. Appl. 14 2 (2002) 151-163
4. Darwish M.A. Hysteresis in Urysohn-Volterra systems. Eur. J. Qual. Theory Diff. Equat. 4 (1999) 1-8
5. Darwish M.A. On a system of nonlinear integral equations with hysteresis. Korean J. Comp. Appl. Math. 6 2 (1999) 305-313
6. Darwish M.A. Global existence and uniqueness of continuous solution of Urysohn-Volterra equation. PU.M.A., Pure Math. Appl. 9 2-3 (1998) 277-282
7. Darwish M.A. On quadratic integral equation of fractional orders. J. Math. Anal. Appl. 311 (2005) 112-119
8. Dugundji J., and Granas A. Fixed Point Theory. Monografie Mathematyczne (1982), PWN, Warsaw
9. El-Sayed W.G., and El-Sayed A.M.A. On the functional integral equations of mixed type and integro-differential equations of fractional orders. Appl. Math. Comput. 154 (2004) 461-467
10. El-Sayed A.M.A. Nonlinear functional differential equations of arbitrary orders. Nonlinear Anal. Theor. Meth. Appl. 33 2 (1998) 181-186
11. El-Sayed A.M.A., and Ibrahim A.-G. Set-valued integral equations of fractional-orders. Appl. Math. Comput. 118 (2001) 113-121
12. Hilfer R. Applications of Fractional Calculus in Physics (2000), World Scientific, Singapore
13. Krasnosel'skii M.A., and Pokrovskii A.V. Systems with Hysteresis (1989), Springer-Verlag, Heidelberg (Russian edition: Nauka, Moscow, 1983)
14. Mayergoyz I.D. Mathematical Models for Hysteresis (1991), Springer-Verlag, New York
15. I. Podlubny, A.M.A. El-Sayed, On two definitions of fractional calculus, Solvak Academy of Science, Institute of Experimental Physics, 1996, UEF-03-96 ISBN 80-7099-252-2.
16. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional Integrals and Derivatives: Theory and Applications (1993), Gordon and Breach Science Publs., Amsterdam (Russian Edition 1987)
17. Visintin A. Differential Models of Hysteresis (1994), Springer-Verlag, New York