Hilfer and Hadamard coupled Volterra fractional integro-differential systems with random effects

. This paper deals with some existence results for two classes of coupled systems of Hilfer and Hilfer-Hadamard random fractional integro-differential equations. The main tool used to carry out our results is Itoh’s random fi xed point theorem.

[1]  S. Abbas,et al.  Implicit Fractional Differential and Integral Equations: Existence and Stability , 2018 .

[2]  Bashir Ahmad,et al.  Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions , 2017 .

[3]  S. Abbas,et al.  A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability , 2017 .

[4]  M. Benchohra,et al.  Measure of noncompactness and impulsive Hadamard fractional implicit differential equations in Banach spaces , 2017 .

[5]  B. Dhage.  Existence theory for first order functional random integrodifferential inclusions , 2017 .

[6]  Ahmed Alsaedi,et al.  Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities , 2017 .

[7]  Ahmed Alsaedi,et al.  A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions , 2016 .

[8]  JinRong Wang,et al.  Nonlocal initial value problems for differential equations with Hilfer fractional derivative , 2015, Appl. Math. Comput..

[9]  N. Tatar,et al.  Well-Posedness and Stability for a Differential Problem with Hilfer-Hadamard Fractional Derivative , 2013 .

[10]  Nasser-eddine Tatar,et al.  Existence and uniqueness for a problem involving Hilfer fractional derivative , 2012, Comput. Math. Appl..

[11]  Nasser-eddine Tatar,et al.  On a Differential Equation Involving Hilfer-Hadamard Fractional Derivative , 2012 .

[12]  A. T. Bharucha-Reid,et al.  Random Integral Equations , 2012 .

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

[14]  Josef Diblík,et al.  Asymptotically periodic solutions of Volterra system of difference equations , 2010, Comput. Math. Appl..

[15]  H. M. Srivastava,et al.  Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions , 2010 .

[16]  Josef Diblík,et al.  Existence of asymptotically periodic solutions of system of Volterra difference equations , 2009 .

[17]  V. Lakshmikantham,et al.  Basic theory of fractional differential equations , 2008 .

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

[19]  A. Granas,et al.  Fixed Point Theory , 2003 .

[20]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[21]  David T. J. Liley,et al.  A continuum theory of electro-cortical activity , 1999, Neurocomputing.

[22]  H. Haken,et al.  Field Theory of Electromagnetic Brain Activity. , 1996, Physical review letters.

[23]  S. Itoh.  Random Fixed Point Theorems in Banach Spaces , 1976 .

[24]  J. Cushing.  Forced Asymptotically Periodic Solutions of Predator-Prey Systems with or without Hereditary Effects , 1976 .

[25]  J. Cowan,et al.  A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue , 1973, Kybernetik.

[26]  S. Abbas,et al.  Partial Hadamard-Stieltjes Fractional Integral Equations in Banach Spaces , 2017 .

[27]  S. Abbas,et al.  SUCCESSIVE APPROXIMATIONS FOR FUNCTIONAL EVOLUTION EQUATIONS AND INCLUSIONS , 2017 .

[28]  R. Kamocki,et al.  On fractional Cauchy-type problems containing Hilfer's derivative , 2016 .

[29]  B. Ahmad,et al.  EXISTENCE OF SOLUTIONS FOR RIEMANN-LIOUVILLLE TYPE COUPLED SYSTEMS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS AND BOUNDARY CONDITIONS , 2016 .

[30]  Donal O'Regan,et al.  Existence results for random fractional differential equations , 2014 .

[31]  M. Kassim.  NON-EXISTENCE OF GLOBAL SOLUTIONS FOR A DIFFERENTIAL EQUATION INVOLVING HILFER FRACTIONAL DERIVATIVE , 2013 .

[32]  Y. Raffoul.  Classification of Positive Solutions of Nonlinear Systems of Volterra Integral Equations , 2011 .

[33]  Tang,et al.  Oscillation Criteria for Two-dimensional Differential Systems , 2010 .

[34]  Anatoly A. Kilbas,et al.  HADAMARD-TYPE FRACTIONAL CALCULUS , 2001 .

[35]  V. Lakshmikantham,et al.  Random differential inequalities , 1980 .

[36]  Chris P. Tsokos,et al.  Random integral equations with applications to life sciences and engineering , 1974 .

[37]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[38]  H. Kober.  ON FRACTIONAL INTEGRALS AND DERIVATIVES , 1940 .