Existence of solutions of the abstract Cauchy problem of fractional order

[1]  Y. Chen,et al.  Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative , 2019, Mathematical Control & Related Fields.

[2]  Doyoon Kim,et al.  L-estimates for time fractional parabolic equations in divergence form with measurable coefficients , 2019, Journal of Functional Analysis.

[3]  M. Muslim,et al.  Approximation of solutions to fractional stochastic integro-differential equations of order α ∈ (1,2] , 2019, Stochastics.

[4]  Zhanbing Bai,et al.  Existence of solutions for some two-point fractional boundary value problems under barrier strip conditions , 2019 .

[5]  On fractional integro-differential inclusions via the extended fractional Caputo–Fabrizio derivation , 2019, Boundary Value Problems.

[6]  D. O’Regan,et al.  Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays , 2019, Mathematica Slovaca.

[7]  M. Benchohra,et al.  On Fractional Integro-differential Equations with State-Dependent Delay and Non-Instantaneous Impulses , 2019, Cubo (Temuco).

[8]  M. Benchohra,et al.  Controllability for Impulsive Fractional Evolution Inclusions with State-Dependent Delay , 2019, Advances in the Theory of Nonlinear Analysis and its Application.

[9]  M. Benchohra,et al.  Semilinear fractional differential equations with infinite delay and non-instantaneous impulses , 2019, Journal of Fixed Point Theory and Applications.

[10]  Rico Zacher Time fractional diffusion equations: solution concepts, regularity, and long-time behavior , 2019, Fractional Differential Equations.

[11]  Kangqun Zhang Existence results for a generalization of the time-fractional diffusion equation with variable coefficients , 2019, Boundary Value Problems.

[12]  J. Sousa,et al.  A new class of mild and strong solutions of integro-differential equation of arbitrary order in Banach space , 2018, 1812.11197.

[13]  Zuomao Yan,et al.  The optimal behavior of solutions to fractional impulsive stochastic integro-differential equations and its control problems , 2018, Journal of Fixed Point Theory and Applications.

[14]  G. N’Guérékata,et al.  On S‐asymptotically ω‐periodic and Bloch periodic mild solutions to some fractional differential equations in abstract spaces , 2018 .

[15]  A. Nazemi,et al.  A New Approach for Solving a Class of Delay Fractional Partial Differential Equations , 2018, Mediterranean Journal of Mathematics.

[16]  Jinrong Wang,et al.  Asymptotically periodic solutions for Caputo type fractional evolution equations , 2018, Fractional Calculus and Applied Analysis.

[17]  D. Chalishajar,et al.  Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces , 2018, Applied System Innovation.

[18]  Existence of the classical and strong solutions for fractional semilinear initial value problems , 2018, Boundary Value Problems.

[19]  K. Sadarangani,et al.  Existence and Uniqueness of Solutions for a Boundary Value Problem of Fractional Type with Nonlocal Integral Boundary Conditions in Hölder Spaces , 2018 .

[20]  Vidushi Gupta,et al.  Functional impulsive differential equation of order α∈(1,2) with nonlocal initial and integral boundary conditions , 2017 .

[21]  P. Muthukumar,et al.  Existence of Solutions and Approximate Controllability of Fractional Nonlocal Neutral Impulsive Stochastic Differential Equations of Order 1 < q < 2 with Infinite Delay and Poisson Jumps , 2017 .

[22]  Jigen Peng,et al.  General fractional differential equations of order $$\alpha \in (1,2)$$α∈(1,2) and Type $$\beta \in [0,1]$$β∈[0,1] in Banach spaces , 2017 .

[23]  Fang Li,et al.  S-Asymptotically $$\varvec{\omega }$$ω-Periodic Mild Solutions of Neutral Fractional Differential Equations with Finite Delay in Banach Space , 2017 .

[24]  Xuping Zhang,et al.  Study on fractional non-autonomous evolution equations with delay , 2017, Comput. Math. Appl..

[25]  Artur Babiarz,et al.  Controllability Problem of Fractional Neutral Systems: A Survey , 2017 .

[26]  Haide Gou,et al.  Weak solutions nonlinear fractional integrodifferential equations in nonreflexive Banach spaces , 2016, Boundary Value Problems.

[27]  Matthias Abend,et al.  Volterra Integral And Functional Equations , 2016 .

[28]  R. Ibrahim,et al.  On mild and strong solutions of fractional differential equations with delay , 2015 .

[29]  H. Henríquez,et al.  Relative controllability of linear systems of fractional order with delay , 2015 .

[30]  L. Caffarelli,et al.  Porous medium flow with both a fractional potential pressure and fractional time derivative , 2015, 1509.06325.

[31]  Donal O'Regan,et al.  On non-autonomous abstract nonlinear fractional differential equations , 2015 .

[32]  Alexis Vasseur,et al.  A Parabolic Problem with a Fractional Time Derivative , 2015, 1501.07211.

[33]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[34]  Nagarajan Sukavanam,et al.  Approximate Controllability of Semilinear Fractional Control Systems of Order α∈(1,2]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \be , 2015, Mediterranean Journal of Mathematics.

[35]  H. Henríquez,et al.  Controllability of Abstract Systems of Fractional Order , 2015 .

[36]  Lishan Liu,et al.  Approximate controllability and optimal controls of fractional evolution systems in abstract spaces , 2014 .

[37]  Vicente Vergara,et al.  Decay estimates for time-fractional and other non-local in time subdiffusion equations in $$\mathbb {R}^d$$Rd , 2014, 1403.1737.

[38]  M. Fabrizio Fractional rheological models for thermomechanical systems. Dissipation and free energies , 2014 .

[39]  On Maximal Regularity and Semivariation of α-Times Resolvent Families* , 2013 .

[40]  B. Achar,et al.  An Alpha-Beta Phase Diagram Representation of the Zeros and Properties of the Mittag-Leffler Function , 2013 .

[41]  G. Jinghuai,et al.  Controllability of Nonlocal Fractional Differential Systems of Order α ∈ (1,2] In Banach Spaces , 2013 .

[42]  Fractional resolvents and fractional evolution equations , 2012 .

[43]  Vahid Johari Majd,et al.  Solution existence for non-autonomous variable-order fractional differential equations , 2012, Math. Comput. Model..

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

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

[46]  Arak M. Mathai,et al.  Mittag-Leffler Functions and Their Applications , 2009, J. Appl. Math..

[47]  H. Brezis Functional Analysis, Sobolev Spaces and Partial Differential Equations , 2010 .

[48]  Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations , 2010 .

[49]  F. Mainardi Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models , 2010 .

[50]  Yury F. Luchko Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation , 2010, Comput. Math. Appl..

[51]  R. Gorenflo,et al.  Fractional Calculus: Integral and Differential Equations of Fractional Order , 2008, 0805.3823.

[52]  J. Douglas Some Applications of Fractional Calculus to Polymer Science , 2007 .

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

[54]  K. Subbarao,et al.  Aged BALB/c Mice as a Model for Increased Severity of Severe Acute Respiratory Syndrome in Elderly Humans , 2005, Journal of Virology.

[55]  Q. Zheng,et al.  On Spectral Inclusions and Approximations of α-times Resolvent Families , 2004 .

[56]  S. I. Piskarev,et al.  Differential Equations in Banach Spaces II. Theory of Cosine Operator Functions , 2004 .

[57]  H. Henríquez,et al.  Differentiability of solutions of the second order abstract Cauchy problem , 2002 .

[58]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

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

[60]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[61]  Francesco Mainardi,et al.  On Mittag-Leffler-type functions in fractional evolution processes , 2000 .

[62]  R. Nagel,et al.  One-parameter semigroups for linear evolution equations , 1999 .

[63]  E. Bazhlekova Subordination principle for fractional evolution equations , 1999 .

[64]  Emilia Bazhlekova,et al.  The abstract Cauchy problem for the fractional evolution equation , 1998 .

[65]  J. Prüss Evolutionary Integral Equations And Applications , 1993 .

[66]  G. Samuel Jordan,et al.  VOLTERRA INTEGRAL AND FUNCTIONAL EQUATIONS (Encyclopedia of Mathematics and its Applications 34) , 1991 .

[67]  H. Fattorini Second Order Linear Differential Equations in Banach Spaces , 1985 .

[68]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[69]  C. C. Travis,et al.  Differentiability of weak solutions to an abstract inhomogeneous differential equation , 1981 .

[70]  C. S. Hönig The Green function of a linear differential equation with a lateral condition , 1973 .

[71]  J. Kisyński,et al.  On cosine operator functions and one-parameter groups of operators , 1972 .

[72]  Edwin Hewitt,et al.  Real And Abstract Analysis , 1967 .

[73]  Philip Hartman,et al.  Self-adjoint, non-oscillatory systems of ordinary, second order, linear differential equations , 1957 .