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Uniqueness results for fredholm type Fractional order Riemann-Liouville integral equations

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Języki publikacji
EN
Abstrakty
EN
In this paper we study the existence and uniqueness of solutions of a certain Fredholm type Riemann-Liouville integral equation of two variables by using Banach contraction principle.
Rocznik
Tom
Strony
5--19
Opis fizyczny
Bibliogr. 33 poz.
Twórcy
autor
  • 2320, Rue de Salaberry, apt 10 Montreal, QC H3M 1K9, Canada
autor
  • Laboratoire de Mathematiques Universite de Sidi Bel-Abbes В.Р. 89, 22000, Sidi Bel-Abbes, Algerie
Bibliografia
  • [1] Abbas S., Benchohra М., Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative, Commun. Math. Anal., 7(2009), 62-72.
  • [2] Abbas S., Benchohra М., Gorniewicz L., Existence theory for impulsive partial hyperbolic functional differential equations involving the Caputo fractional derivative, Sci. Math. Jpn., online e-2010, 271-282. 
  • [3] Abbas S., Benchohra M., N’Guérékata G.M., Topics in Fractional Differential Equations, Springer, New York, 2012.
  • [4] Abbas S., Benchohra M., Vityuk A.N., On fractional order derivatives and Darboux problem for implicit differential equations, Fract. Calc. Appl. Anal., 15(2012), 168-182.
  • [5] Abbas S., Benchohra M., Zhou Y., Fractional order partial hyperbolic functional differential equations with state-dependent delay, Int. J. Dyn. Syst. Differ. Equ., 3(2011), 459-490.
  • [6] Appell J.M., Kalitvin A.S., Zabrejko P.P., Partial Integral Operators and Integrodifferential Equations, 230, Pure and Applied Mathematics Monographs, Marcel and Dekker, Inc., New York, 2000.
  • [7] Belarbi A., Benchohra M., Ouahab A., Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces, Appl. Anal., 85(2006), 1459-1470.
  • [8] Benchohra M., Graef J.R., Hamani S., Existence results for boundary value problems of nonlinear fractional differential equations with integral conditions, Appl. Anal., 87(2008), 851-863.
  • [9] Benchohra M., Hamani S., Ntouyas S.K., Boundary value problems for differential equations with fractional order, Surv. Math. Appl., 3(2008), 1-12.
  • [10] Benchohra M., Henderson J., Ntouyas S.K., Ouahab A., Existence results for functional differential equations of fractional order, J. Math. Anal. Appl., 338(2008), 1340-1350.
  • [11] Bica A., Caus V.A., Muresan S., Application of a trapezoid inequality to neutral Fredholm integro-differential equations in Banach spaces, J. Inequal. Pure Appl. Math., 7(2006), Art. 173.
  • [12] Caballero J., Mingarelli A.B., Sadarangani K., Existence of solutions of an integral equation of Chandrasekhar type in the theory of radiative transfer, Electron. J. Differential Equations, 57(2006), 1-11.
  • [13] Case K.M., Zweifel P.F., Linear Transport Theory, Addison-Wesley, Reading, MA 1967.
  • [14] Cernea A., Arcwise connectedness of the solution set of a nonclosed nonconvex integral inclusion, Miskolc Math. Notes, 9(2008), 33-39.
  • [15] Chandrasekher S., Radiative Transfer, Dover Publications, New York, 1960.
  • [16] Corduneanu C., Integral Equations and Applications, Cambridge University Press, 1991.
  • [17] Diethelm K., Ford N.J., Analysis of fractional differential equations, J. Math. Anal. Appl., 265(2002), 229-248.
  • [18] Glockle W.G., Nonnenmacher T.F., A fractional calculus approach of selfsimilar protein dynamics, Biophys. J., 68(1995), 46-53.
  • [19] Gorniewicz L., Pruszko T., On the set of solutions of the Darboux problem for some hyperbolic equations, Bull. Acad. Polon. Sci. Math. Astronom. Phys., 38(1980), 279-285.
  • [20] Hilfer R., Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [21] Hu S., Khavani M., Zhuang W., Integral equations arrising in the kinetic theory of gases, Appl. Anal., 34(1989), 261-266.
  • [22] Kelly C.T., Approximation of solutions of some quadratic integral equations in transport theory, J. Integral Eq., 4(1982), 221-237.
  • [23] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
  • [24] Mainardi F., Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics, in ”Fractals and Fractional Calculus in Continuum Mechanics” (A. Carpinteri and F. Mainardi, Eds), pp. 291-348, Springer-Verlag, Wien, 1997.
  • [25] Metzler F., Schick W., Kilian H.G., Nonnenmacher T.F., Relaxation in filled polymers: A fractional calculus approach, J. Chem. Phys., 103(1995), 7180-7186.
  • [26] Miller K.S., Ross B., An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
  • [27] Oldham K.B., Spanier J., The Fractional Calculus, Academic Press, New York, London, 1974.
  • [28] Pachpatte B.G., On Volterra-Fredholm integral equation in two variables, Demonstratio Math., XL(2007), 839-852.
  • [29] Pachpatte B.G., On Fredholm type integrodifferential equation, Tamkang J. Math., 39(2008), 85-94.
  • [30] Pachpatte B.G., On Fredholm type integral equation in two variables, Diff. Equ. Appl., 1(2009), 27-39.
  • [31] Podlubny I., Petraš I., Vinagre В.М., O’Leary Р., Dorčak L., Analogue realizations of fractional-order controllers, fractional order calculus and its applications, Nonlinear Dynam., 29(2002), 281-296.
  • [32] Samko S.G., Kilbas A.A., Marichev O.I., Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach, Yverdon, 1993.
  • [33] Vityuk A.N., Golushkov А.V., Existence of solutions of systems of partial differential equations of fractional order, Nonlinear Oscil., 7(2004), 318-325.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-81070072-bef6-45b0-80d2-1131beb29a1c
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