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Keywords:
existence; Hadamard-Caputo derivative; implicit fractional inclusion; convex and nonconvex cases
existence; Hadamard-Caputo derivative; implicit fractional inclusion; convex and nonconvex cases
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.
References:
[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
[2] Abbas, S., Benchohra, M., N’Guérékata, G.M.: Topics in Fractional Differential Equations. Springer, New York, 2012. MR 2962045
[3] Abbas, S., Benchohra, M., N’Guérékata, G.M.: Advanced Fractional Differential and Integral Equations. Nova Science Publishers, New York, 2015. MR 3309582 | Zbl 1314.34002
[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
[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
[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. DOI 10.1007/s10440-008-9356-6 | MR 2596185
[7] Aubin, J.P., Cellina, A.: Differential Inclusions. Springer-Verlag, Berlin-Heidelberg, New York, 1984. Zbl 0538.34007
[8] Aubin, J.P., Frankowska, H.: Set-Valued Analysis. Birkhäuser, Boston, 1990. Zbl 0713.49021
[9] Benchohra, M., Souid, M.S.: Integrable solutions for implicit fractional order differential equations. Transylvanian J. Math. Mechanics 6 (2014), 101–107. MR 3303329
[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. DOI 10.5817/AM2015-2-67 | MR 3367093
[11] Benchohra, M., Souid, M.S.: $L^1$-solutions for implicit fractional order differential equations with nonlocal condition. Filomat 30 (2016), 1485–1492. DOI 10.2298/FIL1606485B | MR 3530093
[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.
[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. DOI 10.1016/0022-247X(91)90164-U
[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.
[15] Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Lecture Notes in Math., vol. 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. DOI 10.1007/BFb0087688 | Zbl 0346.46038
[16] Covitz, H., Nadler, Jr., S.B.: Multivalued contraction mappings in generalized metric spaces. Israel J. Math. 8 (1970), 5–11. DOI 10.1007/BF02771543
[17] Deimling, K.: Multivalued Differential Equations. De Gruyter, Berlin-New York, 1992. Zbl 0820.34009
[18] Granas, A., Dugundji, J.: Fixed Point Theory. Springer-Verlag, New York, 2003. MR 1987179 | Zbl 1025.47002
[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
[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. DOI 10.5817/AM2016-4-263 | MR 3610653
[21] Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore, 2000. Zbl 0998.26002
[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. MR 2218073 | Zbl 1092.45003
[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. DOI 10.1155/S0161171204302231 | MR 2054178 | Zbl 1069.34002
[24] Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego, 1999. Zbl 0924.34008
[25] Zhang, S.: Positive solutions for boundary-value problems of nonlinear fractional differential equations. Electron. J. Differential Equ. 2006 (2006), no. 36, 1–12. MR 2213580 | Zbl 1096.34016
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