Previous |  Up |  Next

Article

Title: Boundary value problems for Hadamard-Caputo implicit fractional differential inclusions with nonlocal conditions (English)
Author: Zahed, Ahmed
Author: Hamani, Samira
Author: Graef, John R.
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 57
Issue: 5
Year: 2021
Pages: 285-297
Summary lang: English
.
Category: math
.
Summary: In this paper, the authors establish sufficient conditions for the existence of solutions to implicit fractional differential inclusions with nonlocal conditions. Both of the cases of convex and nonconvex valued right hand sides are considered. (English)
Keyword: existence
Keyword: Hadamard-Caputo derivative
Keyword: implicit fractional inclusion
Keyword: convex and nonconvex cases
MSC: 26A33
MSC: 34A08
MSC: 34A60
MSC: 34B15
idZBL: Zbl 07442415
idMR: MR4346114
DOI: 10.5817/AM2021-5-285
.
Date available: 2021-10-06T08:59:19Z
Last updated: 2022-02-24
Stable URL: http://hdl.handle.net/10338.dmlcz/149134
.
Reference: [1] Abbas, S., Benchohra, M., Graef, J.R., Henderson, J.: Implicit Fractional Differential and Integral Equations: Existence and Stability.De Gruyter, Berlin, 2018. MR 3791511
Reference: [2] Abbas, S., Benchohra, M., N’Guérékata, G.M.: Topics in Fractional Differential Equations.Springer, New York, 2012. MR 2962045
Reference: [3] Abbas, S., Benchohra, M., N’Guérékata, G.M.: Advanced Fractional Differential and Integral Equations.Nova Science Publishers, New York, 2015. Zbl 1314.34002, MR 3309582
Reference: [4] Adjabi, Y., Jarad, F., Baleanu, D., Abdeljawad, T.: On Cauchy problems with Caputo Hadamard fractional derivatives.J. Comput. Anal. Appl. 21 (2016), 661–681. MR 3495061
Reference: [5] Agarwal, R.P., Benchohra, M., Hamani, S.: Boundary value problems for fractional differential inclusions.Adv. Stud. Contemp. Math. 16 (2008), 181–196. MR 2404634
Reference: [6] Agarwal, R.P., Benchohra, M., Hamani, S.: A survey on existence results for boundary value problems for nonlinear fractional differential equations and inclusions.Acta Appl. Math. 109 (2010), 973–1033. MR 2596185, 10.1007/s10440-008-9356-6
Reference: [7] Aubin, J.P., Cellina, A.: Differential Inclusions.Springer-Verlag, Berlin-Heidelberg, New York, 1984. Zbl 0538.34007
Reference: [8] Aubin, J.P., Frankowska, H.: Set-Valued Analysis.Birkhäuser, Boston, 1990. Zbl 0713.49021
Reference: [9] Benchohra, M., Souid, M.S.: Integrable solutions for implicit fractional order differential equations.Transylvanian J. Math. Mechanics 6 (2014), 101–107. MR 3303329
Reference: [10] Benchohra, M., Souid, M.S.: Integrable solutions for implicit fractional order functional differential equations with infinite delay.Arch. Math. (Brno) 51 (2015), 67–76. MR 3367093, 10.5817/AM2015-2-67
Reference: [11] Benchohra, M., Souid, M.S.: $L^1$-solutions for implicit fractional order differential equations with nonlocal condition.Filomat 30 (2016), 1485–1492. MR 3530093, 10.2298/FIL1606485B
Reference: [12] Bohnenblust, H.F., Karlin, S.: On a theorem of Ville.Contribution to the Theory of Games, Annals of Math. Studies, vol. 24, Princeton University Press, Princeton, 1950, pp. 155–160.
Reference: [13] Byszewski, L.: Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem.J. Math. Anal. Appl. 162 (1991), 494–505. 10.1016/0022-247X(91)90164-U
Reference: [14] Byszewski, L.: Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem.Selected problems of mathematics, , 50th Anniv. Cracow Univ. Technol. Anniv. Issue, 6, Cracow Univ. Technol., Krakow,, 1995, pp. 25–30.
Reference: [15] Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions.Lecture Notes in Math., vol. 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl 0346.46038, 10.1007/BFb0087688
Reference: [16] Covitz, H., Nadler, Jr., S.B.: Multivalued contraction mappings in generalized metric spaces.Israel J. Math. 8 (1970), 5–11. 10.1007/BF02771543
Reference: [17] Deimling, K.: Multivalued Differential Equations.De Gruyter, Berlin-New York, 1992. Zbl 0820.34009
Reference: [18] Granas, A., Dugundji, J.: Fixed Point Theory.Springer-Verlag, New York, 2003. Zbl 1025.47002, MR 1987179
Reference: [19] Guerraiche, N., Hamani, S., Henderson, J.: Boundary value problems for differential inclusions with integral and anti-periodic conditions.Comm. Appl. Nonlinear Anal. 23 (2016), 33–46. MR 3560553
Reference: [20] Guerraiche, N., Hamani, S., Henderson, J.: Initial value problems for fractional functional differential inclusions with Hadamard type derivative.Arch. Math. (Brno) 52 (2016), 263–273. MR 3610653, 10.5817/AM2016-4-263
Reference: [21] Hilfer, R.: Applications of Fractional Calculus in Physics.World Scientific, Singapore, 2000. Zbl 0998.26002
Reference: [22] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations.North-Holland Math. Studies, vol. 204, Elsevier, Amsterdam, 2006. Zbl 1092.45003, MR 2218073
Reference: [23] Momani, S.M., Hadid, S.B., Alawenh, Z.M.: Some analytical properties of solutions of differential equations of noninteger order.Int. J. Math. Math. Sci. 2004 (2004), 697–701. Zbl 1069.34002, MR 2054178, 10.1155/S0161171204302231
Reference: [24] Podlubny, I.: Fractional Differential Equations.Academic Press, San Diego, 1999. Zbl 0924.34008
Reference: [25] Zhang, S.: Positive solutions for boundary-value problems of nonlinear fractional differential equations.Electron. J. Differential Equ. 2006 (2006), no. 36, 1–12. Zbl 1096.34016, MR 2213580
.

Files

Files Size Format View
ArchMathRetro_057-2021-5_2.pdf 472.7Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo