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L1-solutions of the boundary value problem for implicit fractional order differentia equations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to present new results on the existence of solutions for a class of the boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.
Wydawca
Rocznik
Strony
121--128
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
  • Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, Sidi Bel-Abbès, Algeria
  • Department of Economics Sciences, University of Tiaret, Tiaret; and Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, Algeria
Bibliografia
  • [1] S. Abbas, M. Benchohra and G. M. N’Guérékata, Topics in Fractional Differential Equations, Dev. Math. 27, Springer, New York, 2012.
  • [2] R. P. Agarwal, M. Belmekki and M. Benchohra, A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative, Adv. Difference Equ. 2009 (2009), Article ID 981728.
  • [3] R. P. Agarwal, M. Benchohra and S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math. 109 (2010), no. 3, 973-1033.
  • [4] D. Baleanu, K. Diethelm, E. Scalas and J. J. Trujillo, Fractional Calculus, Ser. Complex. Nonlinearity Chaos 3, World Scientific, Hackensack, 2012.
  • [5] M. Benchohra, J. Henderson, S. K. Ntouyas and A. Ouahab, Existence results for fractional order functional differentia equations with infinite delay, J. Math. Anal. Appl. 338 (2008), no. 2, 1340-1350.
  • [6] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), no. 2, 494-505.
  • [7] L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem, in: Selected Problems of Mathematics, 50th Anniv. Cracow Univ. Technol. Anniv. Issue 6, Cracow University of Technology, Cracow (1995), 25-33.
  • [8] L. Byszewski and V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal. 40 (1991), no. 1, 11-19.
  • [9] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
  • [10] A. M. A. El-Sayed and S. A. Abd El-Salam, Lp-solution of weighted Cauchy-type problem of a differ-integral functional equation, Int. J. Nonlinear Sci. 5 (2008), no. 3, 281-288.
  • [11] A. M. A. El-Sayed and H. H. G. Hashem, Integrable and continuous solutions of a nonlinear quadratic integral equation, Electron. J. Qual. Theory Differ. Equ. 2008 (2008), Paper No. 25.
  • [12] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, River Edge, 2000.
  • [13] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006.
  • [14] V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic, Cambridge, 2009.
  • [15] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College, London, 2010.
  • [16] M. D. Ortigueira, Fractional Calculus for Scientists and Engineers, Lect. Notes Electr. Eng. 84, Springer, Dordrecht, 2011.
  • [17] I. Podlubny, Fractional Differential Equations, Math. Sci. Eng. 198, Academic Press, San Diego, 1999.
  • [18] V. E. Tarasov, Fractional dynamics of relativistic particle, Internat. J. Theoret. Phys. 49 (2010), no. 2, 293-303.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-64060d9a-14b3-49c0-b709-d1c1955dc786
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