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2013 | 33 | 1 | 47-63
Tytuł artykułu

Existence and attractivity for fractional order integral equations in Fréchet spaces

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EN
Abstrakty
EN
In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Riemann-Liouville fractional order, by using an extension of the Burton-Kirk fixed point theorem in the case of a Fréchet space.
Twórcy
autor
  • Laboratoire de Mathématiques, Université de Saïda, B.P. 138, 20000, Saïda, Algérie
  • Laboratoire de Mathématiques, Université de Sidi Bel-Abbès, B.P. 89, 22000, Sidi Bel-Abbès, Algérie
Bibliografia
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  • [2] S. Abbas and M. Benchohra, Nonlinear quadratic Volterra Riemann-Liouville integral equations of fractional order, Nonlinear Anal. Forum 17 (2012), 1-9.
  • [3] S. Abbas and M. Benchohra, On the existence and local asymptotic stability of solutions of fractional order integral equations, Comment. Math. 52 (1) (2012), 91-100.
  • [4] S. Abbas, M. Benchohra and J.R. Graef, Integro-differential equations of fractional order, Differ. Equ. Dyn. Syst. 20 (2) (2012), 139-148. doi: 10.1007/s12591-012-0110-1
  • [5] S. Abbas, M. Benchohra and J. Henderson, On global asymptotic stability of solutions of nonlinear quadratic Volterra integral equations of fractional order, Comm. Appl. Nonlinear Anal. 19 (2012), 79-89.
  • [6] S. Abbas, M. Benchohra and G.M. N'Guérékata, Topics in Fractional Differential Equations, Springer, New York, 2012. doi: 10.1007/978-1-4614-4036-9
  • [7] S. Abbas, M. Benchohra and A.N. Vityuk, On fractional order derivatives and Darboux problem for implicit differential equations, Fract. Calc. Appl. Anal. 15 (2) (2012), 168-182.
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  • [9] C. Avramescu and C. Vladimirescu, An existence result of asymptotically stable solutions for an integral equation of mixed type, Electron. J. Qual. Theory Differ. Equ. 25 (2005), 1-6.
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  • [11] D. Baleanu, K. Diethelm, E. Scalas and J.J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific Publishing, New York, 2012.
  • [12] J. Banaś and B.C. Dhage, Global asymptotic stability of solutions of a functional integral equation, Nonlinear Anal. 69 (7) (2008), 1945-1952. doi: 10.1016/j.na.2007.07.038
  • [13] 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. doi: 10.1016/S0022-247X(03)00300-7
  • [14] J. Banaś and T. Zając, Solvability of a functional integral equation of fractional order in the class of functions having limits at infinity, Nonlinear Anal. 71 (2009), 5491-5500. doi: 10.1016/j.na.2009.04.037
  • [15] J. Banaś and T. Zając, A new approach to the theory of functional integral equations of fractional order, J. Math. Anal. Appl. 375 (2011), 375-387. doi: 10.1016/j.jmaa.2010.09.004
  • [16] 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. doi: 10.4134/BKMS.2011.48.3.539
  • [17] B.C. Dhage, Local asymptotic attractivity for nonlinear quadratic functional integral equations, Nonlinear Anal. 70 (2009), 1912-1922. doi: 10.1016/j.na.2008.02.109
  • [18] B.C. Dhage, Global attractivity results for nonlinear functional integral equations via a Krasnoselskii type fixed point theorem, Nonlinear Anal. 70 (2009), 2485-2493. doi: 10.1016/j.na.2008.03.033
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  • [21] A.A. Kilbas, Hari M. Srivastava and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, 2006.
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  • [23] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
  • [24] B.G. Pachpatte, On Volterra-Fredholm integral equation in two variables, Demonstratio Math. XL (4) (2007), 839-852.
  • [25] B.G. Pachpatte, On Fredholm type integral equation in two variables, Differ. Equ. Appl. 1 (2009), 27-39.
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Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1141
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