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Nonlocal three-point multi-term multivalued fractional-order boundary value problems. (English) Zbl 1474.34120

Summary: In this paper we study a new kind of boundary value problems of multi-term fractional differential inclusions and three-point nonlocal boundary conditions. The existence of solutions is established for convex and non-convex multivalued maps by using standard theorems from the fixed point theory. We also construct some examples for demonstrating the application of the main results.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34A08 Fractional ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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[1] B. Ahmad, N. Alghamdi, A. Alsaedi, S.K. Ntouyas,Multi-term fractional differential equations with nonlocal boundary conditions, Open Math.16(2018), 1519-1536. · Zbl 1411.34008
[2] B. Ahmad, M.M. Matar, O.M. El-Salmy,Existence of solutions and Ulam stability for Caputo type sequential fractional differential equations of orderα∈(2,3), Int. J. Anal. Appl.,15 (2017), 86-101. · Zbl 1382.34004
[3] B. Ahmad, A. Alsaedi, S.K. Ntouyas, J. Tariboon,Hadamard-type fractional differential equations, inclusions and inequalities, Springer, Cham, Switzerland, 2017. · Zbl 1370.34002
[4] A. Bressan, G. Colombo,Extensions and selections of maps with decomposable values, Studia Math.,90(1988), 69-86. · Zbl 0677.54013
[5] C. Castaing, M. Valadier,Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. · Zbl 0346.46038
[6] H. Covitz, S. B. Nadler Jr.,Multivalued contraction mappings in generalized metric spaces, Israel J. Math.8(1970), 5-11. · Zbl 0192.59802
[7] K. Deimling,Multivalued Differential Equations, Walter De Gruyter, Berlin-New York, 1992. · Zbl 0760.34002
[8] M. Frigon,Th´eor‘emes d’existence de solutions d’inclusions diff´erentielles, Topological Methods in Differential Equations and Inclusions (edited by A. Granas and M. Frigon), NATO ASI Series C, Vol. 472, Kluwer Acad. Publ., Dordrecht, (1995), 51-87. · Zbl 0834.34021
[9] J.R. Graef, L. Kong, Q. Kong,Application of the mixed monotone operator method to fractional boundary value problems, Fract. Calc. Differ. Calc.,2(2011), 554-567.
[10] A. Granas, J. Dugundji,Fixed Point Theory, Springer-Verlag, New York, 2003. · Zbl 1025.47002
[11] Sh. Hu, N. Papageorgiou,Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, 1997. · Zbl 0887.47001
[12] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo,Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006. · Zbl 1092.45003
[13] M. Kisielewicz,Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991. · Zbl 0731.49001
[14] J. Klafter, S. C Lim, R. Metzler (Editors),Fractional Dynamics in Physics, World Scientific, Singapore, 2011.
[15] M. Korda, D. Henrion, C.N. Jones,Convex computation of the maximum controlled invariant set for polynomial control systems, SIAM J. Control Optim.,52(2014), 2944-2969. · Zbl 1311.49073
[16] A. Lasota, Z. Opial,An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser.Sci. Math. Astronom. Phys.,13(1965), 781-786. · Zbl 0151.10703
[17] C.-G. Li, A. M. Kosti´c, M. Li,Abstract multi-term fractional differential equations, Kragujevac J. Math.,38(2014), 51-71. · Zbl 1465.47033
[18] M. Kosti´c,Abstract Volterra Integro-Differential Equations, CRC Press, Boca Raton, Fl., 2015. · Zbl 1318.45004
[19] Y. Liu,Boundary value problems of singular multi-term fractional differential equations with impulse effects, Math. Nachr.,289(2016), 1526-1547. · Zbl 1354.34021
[20] R.L. Magin,Fractional Calculus in Bioengineering, Begell House Publishers Inc., U.S., 2006.
[21] F.L. Pereira, J. Borges de Sousa, A. Coimbra de Matos,An algorithm for optimal control problems based on differential inclusions, Proceedings of the 34th Conference on Decision & Control, FP05 4:10, New Orleans, LA - December 1995.
[22] Y.Z. Povstenko,Fractional Thermoelasticity, Springer, New York, 2015. · Zbl 1316.74001
[23] B. J. Pr¨uss,Evolutionary Integral Equations and Applications, Birkh¨auser-Verlag, Basel, 1993. · Zbl 0784.45006
[24] S. Stanek,Periodic problem for two-term fractional differential equations, Fract. Calc. Appl. Anal.,20(2017), 662-678 · Zbl 1419.34037
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