Hyers‐Ulam stability analysis to implicit Cauchy problem of fractional differential equations with impulsive conditions

[1]  K. Shah,et al.  On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions , 2017 .

[2]  D. O’Regan,et al.  Mittag–Leffler Stability for Impulsive Caputo Fractional Differential Equations , 2017 .

[3]  Ioan A. Rus,et al.  Ulam stabilities of ordinary differential equations in a Banach space , 2010 .

[4]  T. Rassias.  On the stability of the linear mapping in Banach spaces , 1978 .

[5]  A generalisation of the Malgrange–Ehrenpreis theorem to find fundamental solutions to fractional PDEs , 2017 .

[6]  Robert J. Marks,et al.  Differintegral interpolation from a bandlimited signal's samples , 1981 .

[7]  Yong Zhou,et al.  Ulam’s type stability of impulsive ordinary differential equations☆ , 2012 .

[8]  Zhanbing Bai,et al.  Existence results for the three-point impulsive boundary value problem involving fractional differential equations , 2010, Comput. Math. Appl..

[9]  S. Sivasundaram,et al.  Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations , 2009 .

[10]  A. Cabada,et al.  Positive solutions of nonlinear fractional differential equations with integral boundary value conditions , 2012 .

[11]  Soon-Mo Jung.  On the Hyers–Ulam Stability of the Functional Equations That Have the Quadratic Property☆ , 1998 .

[12]  Arran Fernandez,et al.  An elliptic regularity theorem for fractional partial differential operators , 2018, 1804.01067.

[13]  Existence and Uniqueness Results for Nonlinear Implicit Fractional Dierential Equations with Boundary Conditions , 2014 .

[14]  Ricardo Almeida,et al.  Modeling some real phenomena by fractional differential equations , 2015, 1511.06202.

[15]  R. Hilfer.  Threefold Introduction to Fractional Derivatives , 2008 .

[16]  D. Baleanu,et al.  Stability analysis of Caputo fractional-order nonlinear systems revisited , 2011, Nonlinear Dynamics.

[17]  Dumitru Baleanu,et al.  Solving PDEs of fractional order using the unified transform method , 2018, Appl. Math. Comput..

[18]  Soon-Mo Jung,et al.  Hyers-Ulam stability of linear differential equations of first order, II , 2006, Appl. Math. Lett..

[19]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[20]  M. Benchohra,et al.  On stability for nonlinear implicit fractional differential equations , 2015 .

[21]  R. Bagley,et al.  On the Appearance of the Fractional Derivative in the Behavior of Real Materials , 1984 .

[22]  JinRong Wang,et al.  NONLOCAL IMPULSIVE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TIME-VARYING GENERATING OPERATORS IN BANACH SPACES , 2010 .

[23]  A. Vinodkumar,et al.  Existence, uniqueness and stability of random impulsive fractional differential equations , 2016 .

[24]  D. H. Hyers.  On the Stability of the Linear Functional Equation. , 1941, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[26]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .