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      CONTROLLABILITY OF IMPULSIVE FRACTIONAL EVOLUTION INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES

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      https://www.riss.kr/link?id=A82661034

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      다국어 초록 (Multilingual Abstract)

      According to fractional calculus theory and Banach’s fixed point theorem, we establish the sufficient conditions for the controllability of impulsive fractional evolution integrodifferential equations in Banach spaces. An example is provided to illu...

      According to fractional calculus theory and Banach’s fixed point theorem, we establish the sufficient conditions for the controllability of impulsive fractional evolution integrodifferential equations in Banach spaces. An example is provided to illustrate the theory.

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      목차 (Table of Contents)

      • ABSTRACT
      • 1. INTRODUCTION
      • 2. PRELIMINARIES
      • 3. CONTROLLABILITY RESULT
      • 4. NONLOCAL CONTROLLABILITY RESULT
      • ABSTRACT
      • 1. INTRODUCTION
      • 2. PRELIMINARIES
      • 3. CONTROLLABILITY RESULT
      • 4. NONLOCAL CONTROLLABILITY RESULT
      • 5. EXAMPLE
      • 6. ACKNOWLEDGEMENTS
      • REFERENCES
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      참고문헌 (Reference)

      1 V. Lakshmikantham, "Theory of fractional functional differential equation" 69 : 3337-3343, 2008

      2 V. Lakshmikantham, "Theory of fractional differential equations in a Banach space" 1 (1): 38-45, 2008

      3 V. Lakshmikantham, "Theory of Impulsive Differential Equations" World Scientific, NJ 1989

      4 A. A. Kilbas, "Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204" Elsevier Science B.V., Amsterdam 2006

      5 L. Byszewski, "Theorems about existence and uniqueness of solutions of solutions of a semi-linear evolution nonlocal Cauchy problem" 162 : 494-505, 1991

      6 L. Byszewski, "Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space" 40 : 11-19, 1991

      7 Y. K. Chang, "Some new existence results for fractional differential inclusions with boundary conditions" 49 : 605-609, 2009

      8 J.H. He, "Some applications of nonlinear fractional differential equations and their approximations" 15 (15): 86-90, 1999

      9 Y. Q. Chen, "Robust controllability of interval fractional order linear time invariant systems" 86 : 2794-2802, 2006

      10 K. Balachandran, "Remarks on the paper “Controllability of second order differential inclusion in Banach spaces”" 324 : 746-749, 2006

      1 V. Lakshmikantham, "Theory of fractional functional differential equation" 69 : 3337-3343, 2008

      2 V. Lakshmikantham, "Theory of fractional differential equations in a Banach space" 1 (1): 38-45, 2008

      3 V. Lakshmikantham, "Theory of Impulsive Differential Equations" World Scientific, NJ 1989

      4 A. A. Kilbas, "Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204" Elsevier Science B.V., Amsterdam 2006

      5 L. Byszewski, "Theorems about existence and uniqueness of solutions of solutions of a semi-linear evolution nonlocal Cauchy problem" 162 : 494-505, 1991

      6 L. Byszewski, "Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space" 40 : 11-19, 1991

      7 Y. K. Chang, "Some new existence results for fractional differential inclusions with boundary conditions" 49 : 605-609, 2009

      8 J.H. He, "Some applications of nonlinear fractional differential equations and their approximations" 15 (15): 86-90, 1999

      9 Y. Q. Chen, "Robust controllability of interval fractional order linear time invariant systems" 86 : 2794-2802, 2006

      10 K. Balachandran, "Remarks on the paper “Controllability of second order differential inclusion in Banach spaces”" 324 : 746-749, 2006

      11 Z. Bai, "Positive solutions for boundary value problem of nonlinear fractional differential equations" 311 : 495-505, 2005

      12 E. Hernandez, "On recent developments in the theory of abstract differential equations with fractional derivatives" 73 (73): 3462-3471, 2010

      13 G. M. Mophou, "On integral solutions of some nonlocal fractional differential equations with nondense domain" 71 : 4668-4675, 2009

      14 Y.V. Rogovchenko, "Nonlinear impulsive evolution systems and applications to population models" 207 (207): 300-315, 1997

      15 J.H. Liu, "Nonlinear impulsive evolution equations" 6 (6): 77-85, 1999

      16 S. Zhang, "Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives" 71 : 2087-2093, 2009

      17 G. M. Mophou, "Mild solutions for semilinear fractional differential equations" 2009 (2009): 1-9, 2009

      18 N. Kosmatov, "Integral equations and initial value problems for nonlinear differential equations of fractional order" 70 : 2521-2529, 2009

      19 E. Hernandez, "Impulsive partial neutral differential equations" 19 : 215-222, 2006

      20 V. Lakshmikantham, "General uniqueness and monotone iteration technique in fractional differential equations" 21 : 828-834, 2008

      21 Y. F. Luchko, "Fractional models, nonlocality and complex systems" 59 : 1048-1056, 2010

      22 B. Bonila, "Fractional differential equations as alternative models to nonlinear differential equaitons" 187 : 79-88, 2007

      23 I. Podlubny, "Fractional Differential Equations" Academic Press, New York 1999

      24 F. Mainardi, "Fractional Calculus, Some Basic Problems in Continuum and Statistical Mechanics. In Fractals and Fractional Calculus in Continuum Mechanics" Springer-Verlag, New York 291-348, 1997

      25 JINRONG WANG, "FRACTIONAL NONLOCAL INTEGRODIFFERENTIAL EQUATIONS AND ITS OPTIMAL CONTROL IN BANACH SPACES" 한국산업응용수학회 14 (14): 79-91, 2010

      26 B. Ahmad, "Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations" 3 (3): 251-258, 2009

      27 B. Ahmad, "Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, 2009" 11-, 2009

      28 Y.-K. Chang, "Existence results for impulsive neutral functional differential equations with infinite delay" 2 : 209-218, 2008

      29 M. Benchohra, "Existence results for impulsive multivalued semilinear neutral functional inclusions in Banach spaces" 263 : 763-780, 2001

      30 M. Benchohra, "Existence results for fractional order functional differential equations with infinite delay" 338 : 1340-1350, 2008

      31 K. Balachandran, "Existence results for fractional impulsive integrodifferential equations in Banach spaces" 16 (16): 1970-1977,

      32 M. Benchohra, "Existence results for fractional functional differential inclusions with infinite delay and application to control theory" 11 : 35-56, 2008

      33 R.P. Agarwal, "Existence results for differential equations with fractional order impulses" 44 : 1-21, 2008

      34 B. Ahmad, "Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions" 58 : 1838-1843, 2009

      35 K. Balachandran, "Existence of solutions of abstract fractional impulsive semilinear evolution equations" 2010 (2010): 1-12, 2010

      36 G. M. Mophou, "Existence of mild solution for some fractional differential equations with nonlocal condition" 315-322, 2009

      37 R.P. Agarwal, "Existence of fractional neutral functional differential equations" 59 : 1095-1100, 2010

      38 M. Benchohra, "Existence and uniqueness of solutions to impulsive fractional differential equations, Electronic" 2009 (2009): 1-11, 2009

      39 G.M. Mophou, "Existence and uniqueness of mild solutions to impulsive fractional differential equations" 72 : 1604-1615, 2010

      40 Y. Zhong, "Existence and uniqueness for fractional neutral differential equations with infinite delay" 71 : 3249-3256, 2009

      41 M. Benchohra, "Controllability results for functional semilinear differential inclusions in Fr´echet spaces" 61 : 405-423, 2005

      42 Y.K. Chang, "Controllability of semilinear differential systems with nonlocal initial conditions in Banach spaces" 142 : 267-273, 2009

      43 K. Balachandran, "Controllability of nonlinear systems in Banach spaces: a survey" 115 : 7-28, 2002

      44 Z. Tai, "Controllability of fractional-order impulsive neutral functional infinite delay integrodifferential systems in Banach spaces" 22 (22): 1760-1765, 2009

      45 K. Balachandran, "Controllability of fractional integrodifferential systems in Banach spaces" 3 (3): 363-367, 2009

      46 A. B. Shamardan, "Controllability and observability for fractional control systems" 15 : 25-34, 1999

      47 V. Lakshmikantham, "Basic theory of fractional differential equations" 69 : 2677-2682, 2008

      48 G. Jumarie, "An approach via fractional analysis to non-linearity induced by coarse-graining in space" 11 : 535-546, 2010

      49 K.S. Miller, "An Introduction to the Fractional Calculus and Fractional Differential Equations" John Wiley and Sons, Inc., New York 1993

      50 R.P. Agarwal, "A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative, Advances in Difference Equations, 2009" 47-, 2009

      51 R.P. Agarwal, "A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions" 2010

      52 E. Hernandez, "A second order impulsive Cauchy problem" 31 (31): 451-461, 2002

      53 G.M. N’Gu´er´ekata, "A Cauchy problem for some fractional abstract differential equations with non local conditions" 70 (70): 1873-1876, 2009

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