On Generalized Hyers-Ulam Stability of Admissible Functions

We consider the Hyers-Ulam stability for the following fractional differential equations in sense of Srivastava-Owa fractional operators (derivative and integral) defined in the unit disk: , in a complex Banach space. Furthermore, a generalization of the admissible functions in complex Banach spaces is imposed, and applications are illustrated.

[1]  Rabha W. Ibrahim,et al.  On a fractional integral equation of periodic functions involving Weyl–Riesz operator in Banach algebras , 2008 .

[2]  Zenon Moszner,et al.  On the stability of functional equations , 2009 .

[3]  M. Darus,et al.  Subordination and superordination for analytic functions involving fractional integral operator , 2008 .

[4]  Yongjin Li,et al.  HYERS-ULAM STABILITY OF A POLYNOMIAL EQUATION , 2009 .

[5]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[6]  S. Ulam Problems in modern mathematics , 1964 .

[7]  Shuqin Zhang,et al.  The Existence of a Positive Solution for a Nonlinear Fractional Differential Equation , 2000 .

[8]  Rabha W. Ibrahim,et al.  GENERALIZED ULAM-HYERS STABILITY FOR FRACTIONAL DIFFERENTIAL EQUATIONS , 2012 .

[9]  M. Bidkham,et al.  Hyers-Ulam stability of polynomial equations. , 2010 .

[10]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .

[11]  E. Hille Functional Analysis And Semi-Groups , 1948 .

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

[13]  Rabha W. Ibrahim,et al.  Approximate solutions for fractional differential equation in the unit disk , 2011 .

[14]  Yong Zhou,et al.  Ulam stability and data dependence for fractional differential equations with Caputo derivative , 2011 .

[15]  Existence and uniqueness of holomorphic solutions for fractional Cauchy problem , 2011 .

[16]  M. Rassias Generalised Hyers-Ulam Product-Sum Stability of a Cauchy Type Additive Functional Equation , 2011 .

[17]  Soon-Mo Jung Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis , 2011 .

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

[19]  Gisèle M. Mophou,et al.  Optimal control of fractional diffusion equation , 2011, Comput. Math. Appl..

[20]  Haibo Chen,et al.  Some results on impulsive boundary value problem for fractional differential inclusions , 2011 .

[21]  O. Agrawal Fractional Optimal Control of a Distributed System Using Eigenfunctions , 2007 .

[22]  Rabha W. Ibrahim,et al.  Ulam Stability for Fractional Differential Equation in Complex Domain , 2012 .

[23]  Maslina Darus,et al.  Subordination and superordination for univalent solutions for fractional differential equations , 2008 .

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

[25]  Rabha W. Ibrahim,et al.  On the existence and uniqueness of solutions of a class of fractional differential equations , 2007 .

[26]  George Isac,et al.  Stability of Functional Equations in Several Variables , 1998 .

[27]  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.

[28]  S. Ulam A collection of mathematical problems , 1960 .