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Abstrakty
The present paper deals with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations with Katugampola fractional derivative. The main results are proved by means of Guo-Krasnoselskii and Banach fixed point theorems. For applications purposes, some examples are provided to demonstrate the usefulness of our main results.
Czasopismo
Rocznik
Tom
Strony
35--61
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Laboratory for Pure and Applied Mathematics, University of M’sila, M’sila 28000 ALGERIA
autor
- Laboratory for Pure and Applied Mathematics, University of M’sila, M’sila 28000 ALGERIA
autor
- Laboratory for Pure and Applied Mathematics, University of M’sila, M’sila 28000 ALGERIA
Bibliografia
- [1] Y. Arioua, N. Benhamidouche, Boundary value problem for Caputo-Hadamard fractional differential equations, Surveys in Mathematics and its Applications 12 (2017) 103–115.
- [2] R.P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge, 2001.
- [3] K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, 2010.
- [4] M. El-Shahed, Positive solutions for boundary value problem of nonlinear fractional differential equation, Abstract and Applied Analysis 2007 (2007) 1–8.
- [5] A. Granas, J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
- [6] U.N. Katugampola, New approach to a generalized fractional integral, Applied Mathematics and Computation 218 (3) (2011) 860–865.
- [7] U.N. Katugampola, A new approach to generalized fractional derivatives, Mathematical Analysis and Applications 6 (4) (2014) 1–15.
- [8] U.N. Katugampola, Existence and uniqueness results for a class of generalized fractional differential equations, Bull. Math. Anal. Appl., arXiv:1411.5229v1 (2016).
- [9] A.A. Kilbas, H.H. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, 2006.
- [10] A.A. Kilbas, J.J. Trujillo, Differential equations of fractional order: methods, results and problems I, Appl. Anal. 78 (2001) 153–192.
- [11] A.A. Kilbas, J.J. Trujillo, Differential equations of fractional order: methods, results and problems II, Appl. Anal. 81 (2002) 435–493.
- [12] M.A. Krasnosel’skii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964.
- [13] R.W. Leggett, L.R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana Univ. Math. J. 28 (1979) 673–688.
- [14] K.S. Miller, Fractional differential equations, J. Fract. Calc. 3 (1993) 49–57.
- [15] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
- [16] A.M. Nakhushev, The Sturm–Liouville problem for a second order ordinary differential equation with fractional derivatives in the lower terms, Dokl. Akad. Nauk SSSR 234 (1977) 308–311.
- [17] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York, 1999.
- [18] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integral and Derivatives (Theory and Applications), Gordon and Breach, Switzerland, 1993.
- [19] X. Xu, D. Jiang, C. Yuan, Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation, Nonlinear Anal. 71 (2009) 4676–4688.
- [20] Zhanbing Bai, Haishen L, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. 311 (2005) 495–505.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
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