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On the Existence and Local Asymptotic Stability of Solutions of Fractional Order Integral Equations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we present some results concerning the existence and the local asymptotic stability of solutions for a functional integral equation of fractional order, by using some fixed point theorems.
Rocznik
Strony
91--100
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
autor
Bibliografia
  • [1] S. Abbas, M. Benchohra and G.M. N'Guerekata, Topics in Fractional Differential Equations, Developments in Mathematics, 27, Springer, New York, 2012 (to appear).
  • [2] D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific Publishing, New York, 2012.
  • [3] J. Banaś and I. J. Cabrera, On existence and asymptotic behaviour of solutions of a functional integral equation, Nonlinear Anal. 66 (2007) 2246-2254
  • [4] J. Banaś, J. Caballero, J. Rocha and K. Sadarangant, Monotonie solutions of a class of quadratic integral equations of Volterra type, Comput. Math. Appl. 49 (2005), 943-952.
  • [5] J. Banaś and B.C. Dhage, Global asymptotic stability of solutions of a functional integral equation, Nonlinear Anal. 69 (7) (2008), 1945-1952.
  • [6] J. Banas and K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980.
  • [7] J. Banaś and B. Rzepka, On existence and asymptotic stability of solutions of a nonlinear integral equation, J. Math. Anal. Appl. 284 (2003) 165-173.
  • [8] J. Banaś and B. Rzepka, Monotonie solutions of a quadratic integral equation of fractional order, J. Math. Anal. Appl. 332 (2007) 1371-1379.
  • [9] C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.
  • [10] M. A. Darwish, J. Henderson, and D. O'Regan, Existence and asymptotic stability of solutions of a perturbed fractional functional integral equations with linear modification of the argument, Bull. Korean Math. Soc. 48 (3) (2011), 539-553.
  • [11] B.C. Dhage, Local asymptotic stability for nonlinear quadratic functional integral equations, Electron. J. Qual. Theory Differ. Equ. 10 (2008), 1-13.
  • [12] B.C. Dhage, Local asymptotic attractivity for nonlinear quadratic functional integral equations, Nonlinear Anal. 70 (2009), 1912-1922.
  • [13] B.C. Dhage, Global attractivity restdts for nonlinear functional integral equations via a Krasnoselskii type fixed point theorem, Nonlinear Anal. 70 (2009), 2485-2493.
  • [14] B.C. Dhage, Attractivity and positivity results for nonlinear functional integral equations via measure of noncompactness, Differ. Equ. Appl. 2 (3) (2010), 299-318.
  • [15] A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
  • [16] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [17] A. A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier Science B.V., Amsterdam, 2006.
  • [18] V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.
  • [19] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
  • [20] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [21] V. E. Tarasov, Fractional Dynamics. Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. Springer, Heidelberg, 2010
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0023-0065
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