ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Дифференциальные Уравнения
и
Процессы Управления

Fractional Evolution Integro-differential Equations with Nonlocal Conditions in Banach Spaces

Автор(ы):

M. Chandrasekaran

Professor of Mathematics,
Higher College of Technology,
Muscat,
Sultanate of Oman

m_chands_2000@yahoo.com

V. Dhanapalan

Associate Professor of Mathematics,
Government College of Technology,
Coimbatore-641 013.
Tamilnadu, India.

vdp_vaisu@yahoo.co.in

Аннотация:

In this work, we use the theory of resolvent operators, the fractional powers of operators, fixed point technique and the Gelfand- Shilov principle to establish the existence and uniqueness of local mild and then classical solutions of a class of nonlinear fractional evolution integro-differential equations with nonlocal conditions in Banach space.

Ссылки:

  1. Bahaj. M and Sidki. O.; Almost periodic solutions of semilinear equations with analytic semigroups in Banach spaces, Eletron. J. Differential Equations . 98 (2002), 1-11
  2. Bahuguna. D.; Integrodifferential equations with analytic semigroups, J. Appl. Math. Stochastic Anal. 16 (2) (2003), 177-189
  3. Bahuguna. D and Pani. A. K.; Strong solutions to nonlinear integrodifferential equations, Research Report CMA-R-29-90, Australian National University. (1990)
  4. Bahuguna. D and Raghavendra. V.; Rothe’s method to parabolic initial boundary value problems via abstract parabolic equations, Appl. Anal. 33 (1989), 153-167
  5. Barbu. V.; Integrodifferential equations in Hilbert spaces, An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat. 19 (1973), 265-283
  6. Barbu. V.; Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Buchuresti, Noordholff. (1976)
  7. Barbu. V.; On Nonlinear Volterra integral equations on a Hilbert space, SIAM J. Math. Anal. 8 (1977), 346-355
  8. Bragadi. M and Hazi. M.; Existence and controllability results for an evolution fractional integrodifferential systems, IJCMS. 5 (19) (2010), 901-910
  9. Byszewski. L.; Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505
  10. Crandall. M. G, Londen. S. O. and Nohel. J. A.; An abstract nonlinear Volterra integrodifferential equation, J. Math. Anal. Appl. 64 (1978), 701-735
  11. Debbouche. A.; Fractional Evolution Integrodifferential systems with nonlocal conditions, Adv. in Dyn. Sys. And Appl. 5 (1) (2010), 49-60
  12. Debbouche. A and El-Borai. M. M.; Weak almost periodic and optimal mild solutions of fractional evolution equations, Electron. J. Differential Equations. 46 (2009), 1-8
  13. Deng. K.; Exponential decay of solutions of semilinear parabolic equations with nonlocal conditions, J. Math. Anal. Appl. 179 (1993), 630-637
  14. El-Borai. M. M.; Some probability densities and fundamental solutions of fractional evolution equations, Chaos Solutions Fractals, 14 (3) (2002), 433-440
  15. El-Borai. M. M.; Semigroups and Some nonlinear fractional differential equations, Appl. Math. Comput. 149 (3) (2004), 823-831
  16. El-Borai. M. M.; The fundamental solutions for fractional evolution equations of parabolic type, J. Appl. Math. Stochastic Anal. No. 17(3) (2004), 179-211
  17. El-Borai. M. M.; On some fractional evolution equations with nonlocal conditions, Int. J. Pure Appl. Math. 24 (3) (2005), 405-413
  18. El-Borai. M. M.; On some stochastic fractional integro-differential equations, Adv. Dyn. Syst. Appl. 1 (1) (2006), 49-57
  19. Fitzgibbon. W. E.; Semilinear integrodifferential equations in a Banach space, Nonlinear Anal. 4 (1980), 745-760
  20. Gelfand. I. M and Shilov. G. E.; Generalized Functions, Vol. 1, Moscow, Nauka. (1959)
  21. Heard. M and Ramkin. S. M.; A semilinear parabolic Volterra integrodifferential equation, J. Differential Equations 71 (1988), 201-233
  22. Li. F.; Mild solutions for fractional differential equations with nonlocal conditions, Adv. Difference Equ, Article ID 287861 (2010), 9 pages
  23. Londen. S. O.; On an integral equation in a Hilbert space, SIAM J. Math. Anal. no. 8 (1977), 950-970
  24. Lunardi. A and Sinestari. E.; Fully Nonlinear integrodifferential equations in general Banach spaces, Math. Z. 190 (1985), 225-248
  25. Mophou. G. M and N’Guerekata. G. M.; Mild solutions for Semilinear fractional differential equations, Electron. J. Differential Equations, 21 (2009), 1-9
  26. Pazy. A.; Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer - Verlag. (1983)
  27. Sinestari. E.; Continuous interpolation spaces and special regularity in nonlinear Volterra integrodifferential equations, J. Integral Equations, 5 (1983), 287-308
  28. Yan. Z.; Controllability of semilinear integrodifferential systems with nonlocal conditions, Int. J. Comput. Appl. Math. 2 (3) (2007), 221-236
  29. Webb. G. F.; Abstract Volterra Integrodifferential Equations and a Class of Reaction -Diffusion Equations, Lecture Notes in Mathematics, Vol. 737, Springer-Verlag (1979), 295-303

Полный текст (pdf)