Existence results for an impulsive fractional integro-differential equation with state-dependent delay

In this paper, we have a tendency to implement different fixed point theorem Banach contraction principle, Krasnoselskii's 18 and Schaefer's , 18 coupled with solution operator to analyze the existence and uniqueness results for an impulsive fractional integro-differential equations (IFIDE) with state-dependent delay (SDD) in Banach spaces. Finally, cases are offered to demonstrate the concept.

[1]  Yadollah Ordokhani,et al.  Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations , 2014 .

[2]  Thorsten Gerber,et al.  Semigroups Of Linear Operators And Applications To Partial Differential Equations , 2016 .

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

[4]  V. E. Tarasov.  Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media , 2011 .

[5]  M. Benchohra,et al.  Fractional Integro-Differential Equations with State-Dependent Delay , 2014 .

[6]  Claudio Cuevas,et al.  Existence results for fractional neutral integro-differential equations with state-dependent delay , 2011, Comput. Math. Appl..

[7]  Johnny Henderson,et al.  Impulsive Differential Inclusions: A Fixed Point Approach , 2013 .

[8]  A. Luo,et al.  Fractional Dynamics and Control , 2011 .

[9]  James H. Liu.  NONLINEAR IMPULSIVE EVOLUTION EQUATIONS , 2004 .

[10]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[11]  Claudio Cuevas,et al.  Existence Results for a Fractional Equation with State-Dependent Delay , 2011 .

[12]  M. Benchohra,et al.  Impulsive differential equations and inclusions , 2006 .

[13]  Mohamed Abdalla Darwish,et al.  SEMILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH STATE-DEPENDENT DELAY , 2009 .

[14]  Krishnan Balachandran,et al.  Existence results for impulsive neutral evolution integrodifferential equations with infinite delay , 2009 .

[15]  M. Mallika Arjunan,et al.  Existence Results for Impulsive Neutral Functional Differential Equations With State-Dependent Delay , 2009 .

[16]  Zhi-Wei Lv,et al.  Existence and Uniqueness of Positive Solutions for a Fractional Switched System , 2014 .

[17]  Peiguang Wang,et al.  Oscillatory Criteria for Higher Order Functional Differential Equations with Damping , 2013 .

[18]  JinRong Wang,et al.  Nonlocal impulsive fractional differential inclusions with fractional sectorial operators on Banach spaces , 2015, Appl. Math. Comput..

[19]  Mouffak Benchohra,et al.  On fractional integro-differential inclusions with state-dependent delay in Banach spaces , 2013 .

[20]  Ahmed Alsaedi,et al.  New Existence Results for Nonlinear Fractional Differential Equations with Three-Point Integral Boundary Conditions , 2011 .

[21]  Xiao-Bao Shu,et al.  The existence of mild solutions for impulsive fractional partial differential equations , 2011 .

[22]  Stepan Tersian,et al.  Multiple solutions to boundary value problem for impulsive fractional differential equations , 2014, Fractional Calculus and Applied Analysis.

[23]  Rong Huang,et al.  Existence of solutions for neutral integro-differential equations with state-dependent delay , 2013, Appl. Math. Comput..

[24]  JinRong Wang,et al.  Response to "Comments on the concept of existence of solution for impulsive fractional differential equations [Commun Nonlinear Sci Numer Simul 2014;19: 401-3.]" , 2014, Commun. Nonlinear Sci. Numer. Simul..

[25]  K. Diethelm.  The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

[26]  A. G. Ibrahim,et al.  Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces , 2013 .

[27]  Ivanka M. Stamova,et al.  Stability Analysis of Impulsive Functional Differential Equations , 2009 .

[28]  J. Kwon,et al.  The twisted Daehee numbers and polynomials , 2014 .

[29]  Toufik Guendouzi,et al.  Existence of Mild Solutions for Impulsive Fractional Stochastic Differential Inclusions with State-Dependent Delay , 2014 .

[30]  Jaydev Dabas,et al.  Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay , 2011 .

[31]  Nagarajan Sukavanam,et al.  Existence of Solution for a Second-Order Neutral Differential Equation with State Dependent Delay and Non-instantaneous Impulses , 2014 .

[32]  KHALIDA AISSANI,et al.  IMPULSIVE FRACTIONAL DIFFERENTIAL INCLUSIONS WITH INFINITE DELAY , 2013 .

[33]  I. Podlubny.  Fractional differential equations , 1998 .

[34]  Dumitru Baleanu,et al.  Chaotic incommensurate fractional order Rössler system: active control and synchronization , 2011 .

[35]  C. Kondo,et al.  Existence of traveling waves for diffusive-dispersive conservation laws , 2013 .

[36]  M. J. Mardanov,et al.  Existence and Uniqueness Theorems for Impulsive Fractional Differential Equations with the Two-Point and Integral Boundary Conditions , 2014, TheScientificWorldJournal.

[37]  Ravi P. Agarwal,et al.  On fractional integro-differential equations with state-dependent delay , 2011, Comput. Math. Appl..

[38]  Yong-Kui Chang,et al.  Existence results for impulsive neutral functional differential equations with infinite delay , 2008 .

[39]  Yong Ren,et al.  Existence Results for Impulsive Neutral Stochastic Functional Integro-Differential Equations with Infinite Delays , 2010 .

[40]  Bashir Ahmad,et al.  Comments on the concept of existence of solution for impulsive fractional differential equations , 2014, Commun. Nonlinear Sci. Numer. Simul..

[41]  Caibin Zeng,et al.  Weighted pseudo almost automorphic classical solutions and optimal mild solutions for fractional differential equations and application in fractional reaction–diffusion equations , 2014, Journal of Mathematical Chemistry.

[42]  E. Hernández,et al.  Existence results for an impulsive abstract partial differential equation with state-dependent delay , 2006, Comput. Math. Appl..

[43]  Emilia Bazhlekova,et al.  Fractional evolution equations in Banach spaces , 2001 .

[44]  Mouffak Benchohra,et al.  Semilinear functional differential equations of fractional order with state-dependent delay , 2013 .

[45]  Mouffak Benchohra,et al.  Controllability of Impulsive Fractional Differential Equations with Infinite Delay , 2013 .

[46]  Peiguang Wang,et al.  Generalized Quasilinearization for the System of Fractional Differential Equations , 2013 .

[47]  Velusamy Kavithaa,et al.  Existence results for neutral functional fractional differential equations with state dependent-delay , 2012 .

[48]  Xin Zuo,et al.  Existence and Controllability Results for Fractional Impulsive Integrodifferential Systems in Banach Spaces , 2013 .

[49]  Zuomao Yan,et al.  Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces , 2014 .

[50]  Ahmed Alsaedi,et al.  Existence of solutions for fractional q-integro-difference inclusions with fractional q-integral boundary conditions , 2014 .

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

[52]  Donal O'Regan,et al.  Existence results for differential equation—II , 1991 .

[53]  Drumi D. Bainov,et al.  Impulsive Differential Equations with a Small Parameter , 1994, Series on Advances in Mathematics for Applied Sciences.

[54]  Lishan Liu,et al.  Positive solutions for a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters , 2014 .

[55]  Weigao Ge,et al.  Existence of positive solutions for singular impulsive differential equations with integral boundary conditions , 2014 .

[56]  Mouffak Benchohra,et al.  IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS IN , 2010 .

[57]  Zuomao Yan,et al.  EXISTENCE OF SOLUTIONS TO IMPULSIVE FRACTIONAL PARTIAL NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL INCLUSIONS WITH STATE-DEPENDENT DELAY , 2013 .

[58]  Geraldo M. De Araujo,et al.  Existence of solutions for an Oldroyd model of viscoelastic fluids , 2009 .

[59]  Yong Zhou,et al.  Fractional delay control problems: topological structure of solution sets and its applications , 2014 .

[60]  Ravi P. Agarwal,et al.  Fractional calculus and fractional differential equations in nonreflexive Banach spaces , 2015, Commun. Nonlinear Sci. Numer. Simul..

[61]  Jong Yeoul Park,et al.  Existence results for impulsive neutral stochastic functional integro-differential inclusions with infinite delays , 2014 .

[62]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .