Existence and controllability for nonlinear fractional differential inclusions with nonlocal boundary conditions and time-varying delay

Abstract This paper discusses the existence and controllability of a class of fractional order evolution inclusions with time-varying delay. In the weak topology setting we establish the existence of solutions. Then the controllability of this system with a nonlocal condition is established by applying the Glicksberg-Ky Fan fixed point theorem. As an application, nonlocal problems of a fractional reaction-diffusion equation with a discontinuous nonlinear term is examined.

[1]  On some fractional differential inclusions with random parameters , 2018 .

[2]  Yong-Kui Chang,et al.  Approximate controllability for fractional differential equations of sobolev type via properties on resolvent operators , 2017 .

[3]  On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space , 2015 .

[4]  J. Banaś,et al.  Existence and Asymptotic Behaviour of Solutions of Differential and Integral Equations in Some Function Spaces , 2015 .

[5]  Yi Cheng,et al.  Existence of Solutions for a Class of Nonlinear Evolution Inclusions with Nonlocal Conditions , 2014, J. Optim. Theory Appl..

[6]  Stepan Tersian,et al.  Existence of solutions to boundary value problem for impulsive fractional differential equations , 2014 .

[7]  Yong Zhou.  Basic Theory of Fractional Differential Equations , 2014 .

[8]  A. Ibrahim,et al.  Mild solutions for nonlocal fractional semilinear functional differential inclusions involving Caputo derivative , 2014 .

[9]  Valentina Taddei,et al.  Controllability for systems governed by semilinear evolution inclusions without compactness , 2014 .

[10]  Michal Fečkan,et al.  Controllability of Sobolev type fractional evolution systems , 2014 .

[11]  ON A FRACTIONAL DIFFERENTIAL INCLUSION WITH FOUR-POINT INTEGRAL BOUNDARY CONDITIONS , 2014 .

[12]  Yong Zhou,et al.  Abstract Cauchy problem for fractional functional differential equations , 2013 .

[13]  Nonlocal semilinear evolution equations without strong compactness: theory and applications , 2013 .

[14]  Yong Zhou,et al.  Abstract Cauchy problem for fractional differential equations , 2013 .

[15]  Wenjie Gao,et al.  Existence of solutions for nonlocal p-Laplacian thermistor problems on time scales , 2013 .

[16]  Sotiris K. Ntouyas,et al.  Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions , 2013 .

[17]  Krishnan Balachandran,et al.  On the controllability of fractional dynamical systems , 2012, Int. J. Appl. Math. Comput. Sci..

[18]  Johnny Henderson,et al.  A Filippov’s Theorem, Some Existence Results and the Compactness of Solution Sets of Impulsive Fractional Order Differential Inclusions , 2012 .

[19]  Jin Liang,et al.  Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions , 2012 .

[20]  Juan J. Trujillo,et al.  Controllability of nonlinear fractional dynamical systems , 2012 .

[21]  Rong-Nian Wang,et al.  Abstract fractional Cauchy problems with almost sectorial operators , 2012 .

[22]  Yong Zhou,et al.  Existence and controllability results for fractional semilinear differential inclusions , 2011 .

[23]  Zuomao Yan,et al.  Controllability of fractional-order partial neutral functional integrodifferential inclusions with infinite delay , 2011, J. Frankl. Inst..

[24]  Jin Liang,et al.  A note on the fractional Cauchy problems with nonlocal initial conditions , 2011, Appl. Math. Lett..

[25]  Valeri Obukhovskii,et al.  Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces , 2011 .

[26]  S. Das.  Functional Fractional Calculus , 2011 .

[27]  Ivo Petras,et al.  Fractional-Order Nonlinear Systems , 2011 .

[28]  I. Benedetti,et al.  Semilinear differential inclusions via weak topologies , 2010 .

[29]  R. Agarwal,et al.  A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions , 2010 .

[30]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[31]  D. O’Regan,et al.  EXISTENCE RESULTS FOR SEMILINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH NONLOCAL CONDITIONS , 2009 .

[32]  M. Bettayeb,et al.  New Results on the Controllability and Observability of Fractional Dynamical Systems , 2008 .

[33]  Yangquan Chen,et al.  Robust controllability of interval fractional order linear time invariant systems , 2006, Signal Process..

[34]  Erik Etien,et al.  Control of an induction motor using sliding mode linearization , 2002 .

[35]  F. Rampazzo,et al.  Filippov's and Filippov–Ważewski's Theorems on Closed Domains , 2000 .

[36]  L. Byszewski.  Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem , 1991 .

[37]  H. Brezis.  Analyse fonctionnelle : théorie et applications , 1983 .

[38]  F. Smithies.  Linear Operators , 2019, Nature.

[39]  K. Fan.  Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[40]  I. Glicksberg.  A FURTHER GENERALIZATION OF THE KAKUTANI FIXED POINT THEOREM, WITH APPLICATION TO NASH EQUILIBRIUM POINTS , 1952 .

[41]  A. E. Taylor,et al.  Linear Functionals on Certain Spaces of Abstractly-Valued Functions , 1938 .