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Global attractivity for Volterra type Hadamard fractional integral equations in Fréchet spaces

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Hadamard fractional order. We use an extension of the Burton-Kirk fixed point theorem in Fréchet spaces.
Wydawca
Rocznik
Strony
131--140
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
  • Laboratory of Mathematics, Geometry, Analysis, Control and Applications, Tahar Moulay University of Saïda, P.O. Box 138, EN-Nasr, 20000 Saïda, Algeria
  • Department of Mathematics, Texas A&M University-Kingsville, Kingsville, 78363,USA
autor
  • Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria
autor
  • Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria
Bibliografia
  • [1] Abbas S., Benchohra M., N’Guérékata G. M., Topics in Fractional Differential Equations, Developments in Mathematics, 27, Springer, New York, 2012
  • [2] Abbas S., Benchohra M., N’Guérékata G. M., Advanced Fractional Differential and Integral Equations, Nova Science Publishers, New York, 2015
  • [3] Baleanu D., Diethelm K., Scalas E., Trujillo J. J., Fractional Calculus Models and Numerical Methods, World Scientific Publishing, New York, 2012
  • [4] Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, 2006
  • [5] Miller K. S., Ross B., An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993
  • [6] Lakshmikantham V., Leela S., Vasundhara J., Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009
  • [7] Samko S. G., Kilbas A. A., Marichev O. L., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993
  • [8] Butzer P. L., Kilbas A. A., Trujillo J. J., Fractional calculus in the Mellin setting and Hadamard-type fractional integrals, J. Math. Anal. Appl., 2002, 269, 1-27
  • [9] Butzer P. L., Kilbas A. A., Trujillo J. J., Mellin transform analysis and integration by parts for Hadamard-type fractional integrals, J. Math. Anal. Appl., 2002, 270, 1-15
  • [10] Pooseh S., Almeida R., Torres D., Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative, Numer. Funct. Anal. Optim., 2012, 33(3), 301-319
  • [11] Abbas A., Alaidarous E., Benchohra M., Nieto J. J, Existence and stability of solutions for Hadamard-Stieltjes fractional integral equations, Discrete Dyn. Nat. Soc., 2015, Art. ID 317094
  • [12] Adjabi Y., Jarad F., Baleanu D., Abdeljawad T., On Cauchy problems with Caputo Hadamard fractional derivatives, J. Comput. Anal. Appl., 2016, 21(4), 661-681
  • [13] Aljoudi S., Ahmad B., Nieto J. J., Alsaedi A., A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions, Chaos Solitons Fractals, 2016, 91, 39-46
  • [14] Benchohra M., Bouriah S., Nieto J. J., Existence of periodic solutions for nonlinear implicit Hadamard’s fractional differential equations, Rev. R. Acad. Cienc. Exactas, Fís. Nat. Ser. A Math. RACSAM, 2018, 112, 25-35
  • [15] Gambo Y. Y., Jarad F., Baleanu D., Abdeljawad T., On Caputo modification of the Hadamard fractional derivatives, Adv. Difference Equ., 2014, 2014:10
  • [16] Wang G., Pei K., Baleanu D., Explicit iteration to Hadamard fractional integro-differential equations on infinite domain, Adv. Difference Equ., 2016, 2016:299
  • [17] Abbas S., Benchohra M., Nonlinear quadratic Volterra Riemann-Liouville integral equations of fractional order, Nonlinear Anal. Forum, 2012, 17, 1-9
  • [18] Abbas S., Benchohra M., Fractional order Riemann-Liouville integral equations with multiple time delay, Appl. Math. E-Notes, 2012, 12, 79-87
  • [19] Abbas S., Benchohra M., Henderson J., On global asymptotic stability of solutions of nonlinear quadratic Volterra integral equations of fractional order, Comm. Appl. Nonlinear Anal., 2012, 19, 79-89
  • [20] Abbas S., Benchohra M., Vityuk A. N., On fractional order derivatives and Darboux problem for implicit differential equations, Fract. Calc. Appl. Anal., 2012, 15(2), 168-182
  • [21] Banaś J., Dhage B. C., Global asymptotic stability of solutions of a functional integral equation, Nonlinear Anal., 2008, 69(7), 1945-1952
  • [22] Banaś J., Rzepka B., On existence and asymptotic stability of solutions of a nonlinear integral equation, J. Math. Anal. Appl., 2003, 284, 165-173
  • [23] Banaś J., Zając T., Solvability of a functional integral equation of fractional order in the class of functions having limits at infinity, Nonlinear Anal., 2009, 71, 5491-5500
  • [24] Banaś J., Zając T., A new approach to the theory of functional integral equations of fractional order, J. Math. Anal. Appl., 2011, 375, 375-387
  • [25] Darwish M. A., Henderson J., O’Regan D., Existence and asymptotic stability of solutions of a perturbed fractional functional integral equations with linear modification of the argument, Bull. Korean Math. Soc., 2011, 48(3), 539-553
  • [26] Pachpatte B. G., On Volterra-Fredholm integral equation in two variables, Demonstratio Math., 2007, XL(4), 839-852
  • [27] Pachpatte B. G., On Fredholm type integral equation in two variables, Differ. Equ. Appl., 2009, 1, 27-39
  • [28] Hadamard J., Essai sur L’étude des Fonctions Données par Leur Développment de Taylor, J. Pure Appl. Math., 1892, 4(8), 101-186
  • [29] Frigon M., Granas A., Théorèmes d’Existence pour des Inclusions Différentielles sans Convexité, C. R. Acad. Sci. Paris, Ser. I, 1990, 310, 819-822
  • [30] Avramescu C., Some remarks on a fixed point theorem of Krasnoselskii, Electron. J. Qual. Theory Differ. Equ., 2003, 5, 1-15
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f6d9f72e-c47f-4c47-ba99-00593a2b0a0d
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