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Abstrakty
In this paper, we study the existence of integrable solutions for initial value problems for fractional order implicit differential equations with Hadamard fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.
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Tom
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1--9
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Department of Mathematics, University of Tiaret, Tiaret, Algeria
autor
- Department of Economic Sciences, University of Tiaret, Tiaret
Bibliografia
- [1] S. Abbas, M. Benchohra and G. M. N’Guérékata, Topics in Fractional Differential Equations, Dev. Math. 27, Springer, New York, 2012.
- [2] S. Abbas, M. Benchohra and G. M. N’Guerekata, Advanced Fractional Differential and Integral Equations, Math. Res. Dev., Nova Science, New York, 2015.
- [3] 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.
- [4] 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.
- [5] D. Baleanu, K. Diethelm, E. Scalas and J. J. Trujillo, Fractional Calculus. Models and Numerical Methods, Ser. Complex. Nonlinearity Chaos 3, World Scientific, Hackensack, 2012.
- [6] A. Belarbi, M. Benchohra and A. Ouahab, Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces, Appl. Anal. 85 (2006), no. 12, 1459-1470.
- [7] M. Benchohra, J. Henderson, S. K. Ntouyas and A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. 338 (2008), no. 2, 1340-1350.
- [8] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, New York, 2011.
- [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 diffre-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, Hadamard-type fractional calculus, J. Korean Math. Soc. 38 (2001), no. 6, 1191-1204.
- [14] 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.
- [15] M. Kirane and B. T. Torebek, Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations, Fract. Calc. Appl. Anal. 22 (2019), no. 2, 358-378.
- [16] V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic, Cambridge, 2009.
- [17] L. Ma, Comparison theorems for Caputo-Hadamard fractional differential equations, Fractals 27 (2019), no. 3, Article ID 1950036.
- [18] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity. An Introduction to Mathematical Models, Imperial College, London, 2010.
- [19] M. D. Ortigueira, Fractional Calculus for Scientists and Engineers, Lect. Notes Electr. Eng. 84, Springer, Dordrecht, 2011.
- [20] I. Podlubny, Fractional Differential Equations, Math. Sci. Eng. 198, Academic Press, San Diego, 1999.
- [21] V. E. Tarasov, Fractional dynamics of relativistic particle, Internat. J. Theoret. Phys. 49 (2010), no. 2, 293-303.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
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Bibliografia
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