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Fractional Evolution Integrodifferential Systems with Nonlocal Conditions in Banach Spaces

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International Journal of Computer Applications
© 2014 by IJCA Journal
Volume 96 - Number 12
Year of Publication: 2014
Authors:
V. Dhanapalan
M. Thamilselvan
M. Chandrasekaran
10.5120/16844-6700

V Dhanapalan, M Thamilselvan and M Chandrasekaran. Article: Fractional Evolution Integrodifferential Systems with Nonlocal Conditions in Banach Spaces. International Journal of Computer Applications 96(12):7-13, June 2014. Full text available. BibTeX

@article{key:article,
	author = {V. Dhanapalan and M. Thamilselvan and M. Chandrasekaran},
	title = {Article: Fractional Evolution Integrodifferential Systems with Nonlocal Conditions in Banach Spaces},
	journal = {International Journal of Computer Applications},
	year = {2014},
	volume = {96},
	number = {12},
	pages = {7-13},
	month = {June},
	note = {Full text available}
}

Abstract

This paper is concerned with the proof for the existence and uniqueness of local mild and classical solutions of a class of nonlinear fractional evolution integrodifferential systems with nonlocal conditions in Banach spaces based on the theory of resolvent operators, the fractional powers of operators, fixed point technique and the Gelfand-Shilov principle.

References

  • Bahaj, M and Sidki, O. 2002, Almost periodic solutions of semilinear equations with analytic semigroups in Banach spaces, Electron. J. Diff. Eq, 98, pp. 1-11.
  • Bahuguna, B 2003, Integrodifferential equations with analytic semigroups, J. Appl. Math. Stochastic Anal. 16 (2), pp. 177-189.
  • Bahuguna, D and Pani, A. K. 1990, Strong solutions to nonlinear integrodifferential equations, Research Report CMA-R-29-90, Australian National university.
  • Bahuguna, D. and Raghavendra, V. 1989, Rothe's method to parabolic initial boundary value problems via abstract parabolic equations, Appl. Anal. 33, pp. 153-167.
  • Barbu, V. 1973, Integrodifferential equations in Hilbert spaces, An. Stiint. Univ. Al. I. Cuza Isai Sect. I a Mat. 19, pp. 265-283.
  • Barbu, V. 1977, Nonlinear Semigroups and Differential Equations in Banach spaces, Editura Buchuresti, Noordholff.
  • Barbu, V. 1976, On nonlinear Volterra integral equation in Hilbert space, SIAM J. Math. Anal. 8, pp. 346-355.
  • Bragdi, M and Hazi, M. 2010, Existence and controllabi-lity results for an evolution fractional integrodifferential equations, IJCMS, 5 (19), pp. 901-910.
  • Byszewski, L. 1991, Theorems about the existence and uniqueness of solutions of a semilinear evolution non-local Cauchy problem, J. Math. Anal. Appl. vol. 162, pp. 494-505.
  • Crandall, M. G, Londen, S. O and Nohel, J. A. 1978, An abstract nonlinear Volterra integrodifferential equation, J. Math. Anal. Appl. 64, pp. 701-735.
  • Debbouche, A. 2010, Fractional Evolution Integro-differential systems with nonlocal conditions, Adv. in Dyn. Syn ans Appl, 5(1), pp. 49-60.
  • Debbouche, A and El-Borai, M. M. 2009, Weak almost periodic and optimal mild solutions of fractional evolution equations, Electron. J. Diff. Eq, 46, pp. 1-8.
  • Deng, K. 1993, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl. 179, pp. 630-637.
  • El-Borai, M. M. 2002, Some probability densities and fundamental solutions of fractional evolution equations, Chaos Solitons and Fractals, 14(3), pp. 433-440.
  • El-Borai, M. M. 2004, Semigroups and some nonlinear functional differential equations, Appl. Math. Comput. 149(3), pp. 823-831.
  • El-Borai, M. M. 2004, The fundamental solutions for fractional evolution equations of parabolic type, J. Appl. Math. Stochastic Anal. 17(3), pp. 179-211.
  • El-Borai, M. M. 2005, On some fractional evolution equations with nonlocal conditions, Int. J. Pure Appl. Math. 24(3), pp. 405-413.
  • El-Borai, M. M. 2006, On some stochastic fractional fractional integrodifferential equations, Adv. Dyn. Syst. Appl. 1(1), pp . 49-57.
  • Fitzgibbon, W. E. 1980, Semilinear integrodifferential equations in a Banach space, Nonlinear Anal. 4, pp. 745-760.
  • Gelfand, I. M and Shilov, G. E. 1959, Generalized functions, vol. 1, Moscow, Nauka.
  • Heard, M and Rankin, S. M. 1988, A semilinear parabolic Volterra integrodifferential equation, J. Diff. Eq. 71, pp. 201-233.
  • Li, F. 2010, Mild solutions for fractional differential equations with nonlocal conditions, Adv. Difference Eq, Article ID 287861, 9 pages.
  • Londen, S. O. 1977, On an integral equation in a Hilbert space, SIAM J. Math. Anal. 8, pp. 950-970.
  • Lunardi, A and Sinestari, E. 1985, Fully nonlinear integrodifferential equations in general Banach spaces, Mathematicsche Zeitschrift. 190, pp. 225-248.
  • Mophou, G. M and NGue ´re ´kata, G. M. 2009, Mild solutions for semilinear fractional differential equations, Electron. J. Diff. Eq. 21, pp. 1-9.
  • Pazy, A. 1983, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag.
  • Sinestari, E. 1983, Continuous interpolation spaces and special regularity in nonlinear Volterra integrodifferen-tial equations, J. Integral Eq. 5, pp. 287-308.
  • Webb, G. F. 1979, Abstract Volterra Iintegrodifferential Equations and a Class of Reaction-Diffusion Equations, Lecture Notes in Mathematics, 737, pp. 295-303.
  • Yan, Z. 2007, Controllability of semilinear integrodiffer-ential systems with nonlocal conditions, Int. J. Comput. Appl. Math. 2(3), pp. 221-236.