Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2012 | Vol. 52, [Z] 1 | 91-100
Tytuł artykułu

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

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.
Wydawca

Rocznik
Strony
91-100
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
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
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0023-0065
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.