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A \(k\)-dimensional system of Langevin Hadamard-type fractional differential inclusions with \(2k\) different fractional orders. (English) Zbl 1465.34009

Summary: We investigate the existence of solution for a \(k\)-dimensional system of Langevin Hadamard-type fractional differential inclusions with \(2k\) different fractional orders. We provide an example to illustrate our main result.

MSC:

34A08 Fractional ordinary differential equations
34A60 Ordinary differential inclusions
47N20 Applications of operator theory to differential and integral equations
Full Text: DOI

References:

[1] Agarwal, R. P., O’Regan, D., and Stanek, S.Positive solutions for mixed problems of singular fractional differential equations.Math. Naschr. 285, 1 (2012), 24-71.
[2] Ahmad, B., Alsaedi, A., Ntouyas, S., and Tariboon, J.Hadamard-type fractional differential equations, inclusions and inequalities. vol. xiii ofCham. Springer-Verlag, 2017, pp. 173-208. · Zbl 1370.34002
[3] Ahmad, B., and Nieto, J. J.Solvability of nonlinear Langevin equation involving two fractional orders with Dirichlet boundary conditions.Int. J. Diff. Eq. 2010, Article ID 649486 (2010), 10 pages. · Zbl 1207.34007
[4] Ahmad, B., Nieto, J. J., and Alsaedi, A.A nonlocal three-point inclusion problem of Langevin equation with two different fractional orders.Adv. Diff. Eq. 2012(2012), 2012:54. · Zbl 1291.34004
[5] Ahmad, B., Nieto, J. J., Alsaedi, A., and El-Shahed, M.A study of nonlinear Langevin equation involving two fractional orders in different intervals. Nonlinear Anal. 13(2010), 599-606. · Zbl 1238.34008
[6] Ahmad, B., Ntouyas, S., and Alsaedi, A.Existence results for Langevin fractional differential inclusions involving two fractional orders with four-point multiterm fractional integral boundary conditions.Abst. Appl. Anal. 2013, Article ID 869837 (2013), 17 pages. · Zbl 1276.26008
[7] Ahmad, B., Ntouyas, S., and Alsaedi, A.New results for boundary value problems of Hadamard-type fractional differential inclusions and integral boundary conditions.Bound. Value Probl. 2013(2013), 2013:275. · Zbl 1291.34037
[8] Ahmad, B., Ntouyas, S., and Alsaedi, A.On fractional differential inclusions with with anti-periodic type integral boundary conditions.Bound. Value Probl. 2013(2013), 2013:82. · Zbl 1296.34010
[9] Aljoudi, S., Ahmad, B., Nieto, J. J., and Alsaedi, A.A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions.Chaos Solit. Fract. 91(2016), 39-46. · Zbl 1372.34006
[10] Aubin, J., and Ceuina, A.Differential inclusions: set-valued maps and viability theory. vol. 264 ofFundamental Principles of Mathematical Sciences. Springer-Verlag, 1984, pp. 37-92. · Zbl 0538.34007
[11] Berinde, V., and Pacurar, M.The role of the Pompeiu-Hausdorff metric in fixed point theory.Creat. Math. Inform. 22, 2 (2013), 35-42. · Zbl 1313.47114
[12] Bragdi, M., Debbouche, A., and Baleanu, D.Existence of solutions for fractional differential inclusions with separated boundary conditions in Banach spaces.Adv. Math. Physics 2013, Article ID 426061 (2013), 5 pages. · Zbl 1272.34007
[13] Coffey, W., Kalmykov, Y., and Wadorn, J.The Langevin equation. vol. xxiv ofContemporary Chemical Physics. World Scientific Publishing Co., 2004, pp. 173-208. · Zbl 1098.82001
[14] Covitz, H., and Nadler, S.Multivalued contraction mappings in generalized metric spaces.Israel J. Math. 8(1970), 5-11. · Zbl 0192.59802
[15] Deimling, K.Multi-valued differential equations. vol. xii ofNonlinear Analysis and Applications. Walter de Gruyter Co., Berlin, 1992. · Zbl 0760.34002
[16] Dhage, B.Multi-valued mappings and fixed points.Tamkang J. Math. 37, 1 (2006), 27-46. · Zbl 1108.47046
[17] Hedayati, V., and Rezapour, S.The existence of solution for a k-dimensional system of fractional differential inclusions with anti-periodic boundary value conditions.Filomat 30, 6 (2016), 1601-1613. · Zbl 1474.34099
[18] Kilbas, A., Srivastava, H., and Trujillo, J.Theory and applications of fractional differential equations. vol. 204 ofNorth-Holland Mathematics Studies. Elsevier Science B.V., Amsterdam, 2006. · Zbl 1092.45003
[19] Kisielewicz, M.Differential inclusions and optimal control. vol. 44 ofEast European Series. Kluwer Academic Publishers Group, Dordrecht, 1991. · Zbl 0731.49001
[20] Lasota, A., and Opial, Z.An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations.Bull. Acad. Pol. Sci. Set. Sci. Math. Astronom. Phy. 13(1965), 781-786. · Zbl 0151.10703
[21] Nieto, J., Ouahab, A., and P., P.Extremal solutions and relaxation problems for fractional differential inclusions.Abst. Appl. Anal. 2013, Article ID 292643 (2013), 9 pages. · Zbl 1293.34012
[22] Wang, G., Zhang, L., and Song, G.Boundary value problem of a nonlinear Langevin equation with two different fractional orders and impulses.Fixed Point Theory Appl. 2012(2012), 2012:200. · Zbl 1282.34012
[23] Wang, J., and Ibrahim, A.Existence and controllability results for nonlocal fractional impulsive differential inclusions in Banach spaces.J. Function Sp. 2013, Article ID 518306 (2013), 16 pages. · Zbl 1304.35754
[24] Wax, N.Selected papers on noise and stochastic processes. Dover Publications Inc., New York, 1954 · Zbl 0059.11903
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