TY - JOUR AU - KAVITHA, V. AU - ARJUNAN, M. MALLIKA PY - 2011 TI - CONTROLLABILITY OF IMPULSIVE QUASI-LINEAR FRACTIONAL MIXED VOLTERRA-FREDHOLM-TYPE INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES JO - Journal of Nonlinear Sciences and Applications SP - 152-169 VL - 4 IS - 2 AB - In this paper, we establish a sufficient condition for the controllability of impulsive quasi-linear fractional mixed Volterra-Fredholm-type integrodifferential equations in Banach spaces. The results are obtained by using Banach contraction fixed point theorem combined with the fractional calculus theory. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.004.02.07 DO - 10.22436/jnsa.004.02.07 ID - KAVITHA2011 ER - TY - JOUR TI - Existence results for differential equations with fractional order impulses AU - R. P. Agarwal AU - M. Benchohra AU - B. A. Slimani JO - Memoirs on Differential Equations and Mathematical Physics PY - 2008 DA - 2008// VL - 44 ID - Agarwal2008 ER - TY - JOUR TI - A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative AU - R. P. Agarwal AU - M. Belmekki AU - M. Benchohra JO - Advances in Difference Equations, Article ID 981728 PY - 2009 DA - 2009// VL - 2009 ID - Agarwal2009 ER - TY - JOUR TI - A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions AU - R. P. Agarwal AU - M. Benchohra AU - S. Hamani JO - Acta Appl. Math. PY - 2010 DA - 2010// VL - 109(3) ID - Agarwal2010 ER - TY - JOUR TI - Existence of fractional neutral functional differential equations AU - R. P. Agarwal AU - Y. Zhou AU - Y. He JO - Comp. Math. Appl. PY - 2010 DA - 2010// VL - 59 ID - Agarwal2010 ER - TY - JOUR TI - Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations AU - B. Ahmad AU - S. Sivasundaram JO - Nonlinear Analysis: Hybrid Systems PY - 2009 DA - 2009// VL - 3(3) ID - Ahmad2009 ER - TY - JOUR TI - Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions AU - B. Ahmad AU - J. J. Nieto JO - Comp. Math. Appl PY - 2009 DA - 2009// VL - 58 ID - Ahmad2009 ER - TY - JOUR TI - Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions AU - B. Ahmad AU - J. J. Nieto JO - Article ID 708576. PY - 2009 DA - 2009// VL - 2009 ID - Ahmad2009 ER - TY - JOUR TI - Quasilinear evolution equations and parabolic systems AU - H. Amann JO - Trans. Amer. Math. Soc. PY - 1986 DA - 1986// VL - 29 ID - Amann1986 ER - TY - JOUR TI - Quasilinear integrodifferential equations in Banach spaces AU - D. Bahuguna JO - Nonlinear Anal. PY - 1995 DA - 1995// VL - 24 ID - Bahuguna1995 ER - TY - JOUR TI - Positive solutions for boundary value problem of nonlinear fractional differential equations AU - Z. Bai AU - H. Lü JO - J. Math. Anal. Appl. PY - 2005 DA - 2005// VL - 311 ID - Bai2005 ER - TY - JOUR TI - Existence of solutions of quasilinear integrodifferential equations with nonlocal condition AU - K. Balachandran AU - K. Uchiyama JO - Tokyo. J. Math. PY - 2000 DA - 2000// VL - 23 ID - Balachandran2000 ER - TY - JOUR TI - Existence of solutions for quasilinear delay integrodifferential equations with nonlocal conditions AU - K. Balachandran AU - F. P. Samuel JO - Electronic Journal of Differential Equations PY - 2009 DA - 2009// VL - 2009 ID - Balachandran2009 ER - TY - JOUR TI - Existence of mild solutions for quasilinear integrodifferential equations with impulsive conditions AU - K. Balachandran AU - F. P. Samuel JO - Electronic Journal of Differential Equations PY - 2009 DA - 2009// VL - 2009(84) ID - Balachandran2009 ER - TY - JOUR TI - Controllability of nonlocal impulsive quasi- linear integrodifferential systems in Banach spaces AU - K. Balachandran AU - J. Y. Park AU - S. H. Park JO - Reports on Mathematical Physics PY - 2010 DA - 2010// VL - 65(2) ID - Balachandran2010 ER - TY - JOUR TI - Controllability of nonlinear systems in Banach spaces: a survey AU - K. Balachandran AU - J. P. Dauer JO - J. Optim. Theory Appl. PY - 2002 DA - 2002// VL - 115 ID - Balachandran2002 ER - TY - JOUR TI - Remarks on the paper ''Controllability of second order differential inclusion in Banach spaces[J. Math. Anal. Appl. 285, 537-550 (2003)]. AU - K. Balachandran AU - J. H. Kim JO - J. Math. Anal. Appl. PY - 2006 DA - 2006// VL - 324 ID - Balachandran2006 ER - TY - JOUR TI - Controllability of fractional integrodifferential systems in Banach spaces AU - K. Balachandran AU - J. Y. Park JO - Nonlinear Analysis: Hybrid Systems PY - 2009 DA - 2009// VL - 3(4) ID - Balachandran2009 ER - TY - JOUR TI - Existence of solutions of abstract fractional impulsive semilinear evolution equations AU - K. Balachandran AU - S. Kiruthika JO - Electronic Journal of Qualitative Theory of Differential Equations PY - 2010 DA - 2010// VL - 2010(4) ID - Balachandran2010 ER - TY - BOOK TI - Existence results for fractional impulsive integrodifferential equations in Banach spaces AU - K. Balachandran AU - S. Kiruthika AU - J. J. Trujillo PB - Commun Nonlinear Sci Numer Simulat PY - 2010 DA - 2010// CY - doi:10.1016/j.cnsns.2010.08.005. ID - Balachandran2010 ER - TY - JOUR TI - Existence and uniqueness of solutions to impulsive fractional differential equations AU - M. Benchohra AU - B. A. Slimani JO - Electronic Journal of Differential Equations PY - 2009 DA - 2009// VL - 2009(10) ID - Benchohra2009 ER - TY - JOUR TI - Existence results for fractional functional differential inclusions with infinite delay and application to control theory AU - M. Benchohra AU - J. Henderson AU - S. K. Ntouyas AU - A. Ouahab JO - Fract. Calc. Appl. Anal. PY - 2008 DA - 2008// VL - 11 ID - Benchohra2008 ER - TY - JOUR TI - Existence results for impulsive multivalued semilinear neutral functional inclusions in Banach spaces AU - M. Benchohra AU - J. Henderson AU - S. K. Ntouyas JO - J. Math. Anal. Appl. PY - 2001 DA - 2001// VL - 263 ID - Benchohra2001 ER - TY - JOUR TI - Existence results for fractional order functional differential equations with infinite delay AU - M. Benchohra AU - J. Henderson AU - S. K. Ntouyas AU - A. Ouahab JO - J. Math. Anal. Appl. PY - 2008 DA - 2008// VL - 338 ID - Benchohra2008 ER - TY - JOUR TI - Controllability results for functional semilinear differential inclusions in Fréchet spaces AU - M. Benchohra AU - A. Ouahab JO - Nonlinear Anal. PY - 2005 DA - 2005// VL - 61 ID - Benchohra2005 ER - TY - JOUR TI - Fractional differential equations as alternative models to nonlinear differential equations AU - B. Bonila AU - M. Rivero AU - L. Rodriquez-Germa AU - J. J. Trujilio JO - Appl. Math. Comput. PY - 2007 DA - 2007// VL - 187 ID - Bonila2007 ER - TY - JOUR TI - Theorems about existence and uniqueness of solutions of solutions of a semi- linear evolution nonlocal Cauchy problem AU - L. Byszewski JO - J. Math. Anal. Appl. PY - 1991 DA - 1991// VL - 162 ID - Byszewski 1991 ER - TY - JOUR TI - Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space AU - L. Byszewski AU - V. Lakshmikantham JO - Appl. Anal. PY - 1991 DA - 1991// VL - 40 ID - Byszewski1991 ER - TY - JOUR TI - Nonlocal Cauchy problem for quasilinear integrodifferential equations in Banach spaces AU - M. Chandrasekaran JO - Electronic Journal of Differential Equations PY - 2007 DA - 2007// VL - 2007(33) ID - Chandrasekaran2007 ER - TY - JOUR TI - Some new existence results for fractional differential inclusions with boundary conditions AU - Y. K. Chang AU - J. J. Nieto JO - Math. Comput. Modelling PY - 2009 DA - 2009// VL - 49 ID - Chang2009 ER - TY - JOUR TI - Controllability of mixed Volterra Fredholm type integrodifferential inclusions in Banach spaces AU - Y.-K. Chang AU - D. N. Chalishajar JO - Journal of the Franklin Institute PY - 2008 DA - 2008// VL - 345(5) ID - Chang2008 ER - TY - JOUR TI - Existence results for impulsive neutral functional differential equations with infinite delay AU - Y.-K. Chang AU - A. Anguraj AU - M. Mallika Arjunan JO - Nonlinear Analysis: Hybrid Systems PY - 2008 DA - 2008// VL - 2 ID - Chang2008 ER - TY - JOUR TI - Controllability of semilinear differential systems with nonlocal initial conditions in Banach spaces AU - Y. K. Chang AU - J. J. Nieto AU - W. S. Li JO - J. Optim. Theory Appl. PY - 2009 DA - 2009// VL - 142 ID - Chang2009 ER - TY - JOUR TI - Robust controllability of interval fractional order linear time invariant systems AU - Y. Q. Chen AU - H. S. Ahu AU - D. Xue JO - Signal Processing PY - 2006 DA - 2006// VL - 86 ID - Chen2006 ER - TY - JOUR TI - On a quasilinear functional integrodifferential equations in a Banach space AU - M. B. Dhakne AU - B. G. Pachpatte JO - Indian J. Pure Appl. Math. PY - 1994 DA - 1994// VL - 25 ID - Dhakne1994 ER - TY - JOUR TI - Quasilinear nonlocal integrodifferential equations in Banach spaces AU - Q. Dong AU - G. Li AU - J. Zhang JO - Electronic Journal of Differential Equations PY - 2008 DA - 2008// VL - 2008(19) ID - Dong2008 ER - TY - JOUR TI - A Cauchy problem for some fractional abstract differential equations with non local conditions AU - G. M. N'Guérékata JO - Nonlinear Analysis PY - 2009 DA - 2009// VL - 70(5) ID - N'Guérékata2009 ER - TY - JOUR TI - Some applications of nonlinear fractional differential equations and their approximations AU - J. H. He JO - Bull. Sci. Technol. PY - 1999 DA - 1999// VL - 15(2) ID - He 1999 ER - TY - JOUR TI - On recent developments in the theory of abstract differential equations with fractional derivatives AU - E. Hernandez AU - Donal O'Regan AU - K. Balachandran JO - Nonlinear Analysis: Theory, Methods and Applications PY - 2010 DA - 2010// VL - 73(15) ID - Hernandez2010 ER - TY - JOUR TI - A second order impulsive Cauchy problem AU - E. Hernandez JO - Int. J. Math. Math. Sci. PY - 2002 DA - 2002// VL - 31(8) ID - Hernandez2002 ER - TY - JOUR TI - Impulsive partial neutral differential equations AU - E. Hernandez AU - H. R. Henriquez JO - Appl. Math. Lett. PY - 2006 DA - 2006// VL - 19 ID - Hernandez2006 ER - TY - JOUR TI - An approach via fractional analysis to non-linearity induced by coarse-graining in space AU - G. Jumarie JO - Nonlinear Anal. RWA PY - 2010 DA - 2010// VL - 11 ID - Jumarie2010 ER - TY - JOUR TI - Nonhomogeneous quasilinear evolution equations in Banach spaces AU - S. Kato JO - Nonlinear Anal. PY - 1985 DA - 1985// VL - 9 ID - Kato1985 ER - TY - BOOK TI - Theory and Applications of Fractional Differential Equations AU - A. A. Kilbas AU - Hari M. Srivastava AU - Juan J. Trujillo PB - North-Holland Mathematics Studies, 204. Elsevier Science B.V., PY - 2006 DA - 2006// CY - Amsterdam ID - Kilbas2006 ER - TY - JOUR TI - Integral equations and initial value problems for nonlinear differential equations of fractional order AU - N. Kosmatov JO - Nonlinear Analysis PY - 2009 DA - 2009// VL - 70 ID - Kosmatov2009 ER - TY - BOOK TI - Theory of Impulsive Differential Equations AU - V. Lakshmikantham AU - D. D. Bainov AU - P. S. Simeonov PB - World Scientific PY - 1989 DA - 1989// CY - NJ ID - Lakshmikantham1989 ER - TY - JOUR TI - Theory of fractional functional differential equation AU - V. Lakshmikantham JO - Nonlinear Anal. PY - 2008 DA - 2008// VL - 69 ID - Lakshmikantham2008 ER - TY - JOUR TI - Theory of fractional differential equations in a Banach space AU - V. Lakshmikantham AU - J. V. Devi JO - Eur. J. Pure Appl. Math. PY - 2008 DA - 2008// VL - 1(1) ID - Lakshmikantham2008 ER - TY - JOUR TI - Basic theory of fractional differential equations AU - V. Lakshmikantham AU - A. S. Vatsala JO - Nonlinear Anal. PY - 2008 DA - 2008// VL - 69 ID - Lakshmikantham2008 ER - TY - JOUR TI - General uniqueness and monotone iteration technique in fractional differential equations AU - V. Lakshmikantham AU - A. S. Vatsala JO - Appl. Math. Lett. PY - 2008 DA - 2008// VL - 21 ID - Lakshmikantham2008 ER - TY - JOUR TI - Nonlinear impulsive evolution equations AU - J. H. Liu JO - Dyn. Contin. Discrete Impuls. Syst. PY - 1999 DA - 1999// VL - 6(1) ID - Liu1999 ER - TY - JOUR TI - Fractional models, nonlocality and complex systems AU - Y. F. Luchko AU - M. Rivero AU - J. J. Trujillo AU - M. P. Velasco JO - Comp. Math. Appl. PY - 2010 DA - 2010// VL - 59 ID - Luchko2010 ER - TY - JOUR TI - Fractional Calculus, Some Basic Problems in Continuum and Statistical Mechanics AU - F. Mainardi JO - in A. Carpinteri, F. Mainardi (Eds)., Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, New York PY - 1997 DA - 1997// VL - ID - Mainardi 1997 ER - TY - BOOK TI - An Introduction to the Fractional Calculus and Fractional Differential Equations AU - K. S. Miller AU - B. Ross PB - John Wiley and Sons, Inc. PY - 1993 DA - 1993// CY - New York ID - Miller1993 ER - TY - JOUR TI - Existence of mild solution for some fractional differential equations with nonlocal condition AU - G. M. Mophou AU - G. M. N'Guérékata JO - Semigroup Forum PY - 2009 DA - 2009// VL - 79 ID - Mophou2009 ER - TY - JOUR TI - On integral solutions of some nonlocal fractional differential equations with nondense domain AU - G. M. Mophou AU - G. M. N'Guérékata JO - Nonlinear Analysis PY - 2009 DA - 2009// VL - 71 ID - Mophou2009 ER - TY - JOUR TI - Mild solutions for semilinear fractional differential equations AU - G. M. Mophou AU - G. M. N'Guérékata JO - Electronic Journal of Differential Equations PY - 2009 DA - 2009// VL - 2009(21) ID - Mophou2009 ER - TY - JOUR TI - Existence and uniqueness of mild solutions to impulsive fractional differential equations AU - G. M. Mophou JO - Nonlinear Analysis PY - 2010 DA - 2010// VL - 72 ID - Mophou2010 ER - TY - BOOK TI - Fractional Differential Equations AU - I. Podlubny PB - Academic Press PY - 1999 DA - 1999// CY - New York ID - Podlubny1999 ER - TY - JOUR TI - Abstract quasilinear Volterra integrodifferential equations AU - H. Oka JO - Nonlinear Anal. PY - 1997 DA - 1997// VL - 28 ID - Oka1997 ER - TY - JOUR TI - Abstract quasilinear integrodifferential equtions of hyperbolic type AU - H. Oka AU - N. Tanaka JO - Nonlinear Anal. PY - 1997 DA - 1997// VL - 29 ID - Oka1997 ER - TY - JOUR TI - Nonlinear impulsive evolution systems and applications to population models AU - Y. V. Rogovchenko JO - J. Math. Anal. Appl. PY - 1997 DA - 1997// VL - 207(2) ID - Rogovchenko1997 ER - TY - JOUR TI - Abstract quasilinear equations of evolution in nonreflexive Banach spaces AU - N. Sanekata JO - Hiroshima Mathematical Journal PY - 1989 DA - 1989// VL - 19 ID - Sanekata1989 ER - TY - JOUR TI - Controllability and observability for fractional control systems AU - A. B. Shamardan AU - M. R. A. Moubarak JO - Journal of Fractional Calculus PY - 1999 DA - 1999// VL - 15 ID - Shamardan1999 ER - TY - JOUR TI - Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces AU - Z. Tai AU - X. Wang JO - Applied Mathematics Letters PY - 2009 DA - 2009// VL - 22(11) ID - Tai2009 ER - TY - JOUR TI - Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives AU - S. Zhang JO - Nonlinear Anal. PY - 2009 DA - 2009// VL - 71 ID - Zhang2009 ER - TY - JOUR TI - Existence and uniqueness for fractional neutral differential equations with infinite delay AU - Y. Zhong AU - J. Feng AU - J. Li JO - Nonlinear Anal. PY - 2009 DA - 2009// VL - 71 ID - Zhong2009 ER -