参考文献:1.Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)MATH 2.Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V, Amsterdam (2006)MATH 3.Sabatier, J., Agrawal, O.P., Machado, J.A.T. (eds.): Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007) 4.Tomovski, Z., Hilfer, R., Srivastava, H.M.: Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions. Integral Transf. Spec. Funct. 21, 797–814 (2010)MathSciNet CrossRef MATH 5.Konjik, S., Oparnica, L., Zorica, D.: Waves in viscoelastic media described by a linear fractional model. Integral Transf. Spec. Funct. 22, 283–291 (2011)MathSciNet CrossRef MATH 6.Keyantuo, V., Lizama, C.: A characterization of periodic solutions for time-fractional differential equations in UMD spaces and applications. Math. Nach. 284, 494–506 (2011)MathSciNet CrossRef MATH 7.Ahmad, B., Nieto, J.J.: Riemann–Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions. Bound. Value Probl. 36, 1–9 (2011)MathSciNet 8.Liang, S., Zhang, J.: Existence of multiple positive solutions for m-point fractional boundary value problems on an infinite interval. Math. Comput. Model. 54, 1334–1346 (2011)MathSciNet CrossRef MATH 9.Su, X.: Solutions to boundary value problem of fractional order on unbounded domains in a Banach space. Nonlinear Anal. 74, 2844–2852 (2011)MathSciNet CrossRef MATH 10.Bai, Z.B., Sun, W.: Existence and multiplicity of positive solutions for singular fractional boundary value problems. Comput. Math. Appl. 63, 1369–1381 (2012)MathSciNet CrossRef MATH 11.Agarwal, R.P., O’Regan, D., Stanek, S.: Positive solutions for mixed problems of singular fractional differential equations. Math. Nachr. 285, 27–41 (2012)MathSciNet CrossRef MATH 12.Cabada, A., Wang, G.: Positive solutions of nonlinear fractional differential equations with integral boundary value conditions. J. Math. Anal. Appl. 389, 403–411 (2012)MathSciNet CrossRef MATH 13.Ahmad, B., Ntouyas, S.K., Alsaedi, A.: A study of nonlinear fractional differential equations of arbitrary order with Riemann–Liouville type multistrip boundary conditions. Math. Probl. Eng., Art. ID 320415, 9 (2013) 14.Zhang, L., Wang, G., Ahmad, B., Agarwal, R.P.: Nonlinear fractional integro-differential equations on unbounded domains in a Banach space. J. Comput. Appl. Math. 249, 51–56 (2013)MathSciNet CrossRef MATH 15.Ahmad, B., Ntouyas, S.K.: Existence results for higher order fractional differential inclusions with multi-strip fractional integral boundary conditions. Electron. J. Qual. Theory Differ. Equ. 20, 1–19 (2013)MathSciNet CrossRef 16.O’Regan, D., Stanek, S.: Fractional boundary value problems with singularities in space variables. Nonlinear Dyn. 71, 641–652 (2013)MathSciNet CrossRef MATH 17.Graef, J.R., Kong, L., Wang, M.: Existence and uniqueness of solutions for a fractional boundary value problem on a graph. Fract. Calc. Appl. Anal. 17, 499–510 (2014)MathSciNet CrossRef MATH 18.Wang, G., Liu, S., Zhang, L.: Eigenvalue problem for nonlinear fractional differential equations with integral boundary conditions. Abstr. Appl. Anal., Art. ID 916260, 6 (2014) 19.Ahmad, B., Agarwal, R.P.: Some new versions of fractional boundary value problems with slit-strips conditions. Bound. Value Probl. 2014, 175 (2014)MathSciNet CrossRef 20.Liu, X., Liu, Z.: Existence results for fractional semilinear differential inclusions in Banach spaces. J. Appl. Math. Comput. 42, 171–182 (2013)MathSciNet CrossRef MATH 21.Liu, X., Liu, Z.: Existence results for fractional differential inclusions with multivalued term depending on lower-order derivative. Abstr. Appl. Anal., Art. ID 423796, 24 (2012) 22.Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley and Sons, New York (1993)MATH 23.Wei, Z., Dong, W.: Periodic boundary value problems for Riemann-Liouville sequential fractional differential equations. Electron. J. Qual. Theory Differ. Equ. 87, 1–13 (2011)MathSciNet CrossRef 24.Wei, Z., Li, Q., Che, J.: Initial value problems for fractional differential equations involving Riemann–Liouville sequential fractional derivative. J. Math. Anal. Appl. 367, 260–272 (2010)MathSciNet CrossRef MATH 25.Klimek, M.: Sequential fractional differential equations with Hadamard derivative. Commun. Nonlinear Sci. Numer. Simul. 16, 4689–4697 (2011)MathSciNet CrossRef MATH 26.Baleanu, D., Mustafa, O.G., Agarwal, R.P.: On L\(^p\) -solutions for a class of sequential fractional differential equations. Appl. Math. Comput. 218, 2074–2081 (2011)MathSciNet CrossRef MATH 27.Bai, C.: Impulsive periodic boundary value problems for fractional differential equation involving Riemann–Liouville sequential fractional derivative. J. Math. Anal. Appl. 384, 211–231 (2011)MathSciNet CrossRef MATH 28.Ahmad, B., Nieto, J.J.: Sequential fractional differential equations with three-point boundary conditions. Comput. Math. Appl. 64, 3046–3052 (2012)MathSciNet CrossRef MATH 29.Ahmad, B., Nieto, J.J.: Boundary value problems for a class of sequential integrodifferential equations of fractional order. J. Funct. Spaces Appl., Art. ID 149659, 8 (2013) 30.Ahmad, B., Ntouyas, S.K.: On higher-order sequential fractional differential inclusions with nonlocal three-point boundary conditions. Abstr. Appl. Anal., Art. ID 659405, 10 (2014) 31.Deimling, K.: Multivalued Differential Equations. Walter De Gruyter, Berlin (1992)CrossRef MATH 32.Hu, Sh, Papageorgiou, N.: Handbook of Multivalued Analysis, Theory I. Kluwer, Dordrecht (1997)CrossRef 33.Covitz, H., Nadler Jr, S.B.: Multivalued contraction mappings in generalized metric spaces. Israel J. Math. 8, 5–11 (1970)MathSciNet CrossRef MATH 34.Kisielewicz, M.: Differential Inclusions and Optimal Control. Kluwer, Dordrecht (1991)MATH 35.Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580. Springer, Berlin (1977)CrossRef 36.Lasota, A., Opial, Z.: 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, 781–786 (1965)MathSciNet MATH 37.Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2005) 38.Bressan, A., Colombo, G.: Extensions and selections of maps with decomposable values. Studia Math. 90, 69–86 (1988)MathSciNet MATH 39.Frigon, M.: Théorèmes d’existence de solutions d’inclusions différentielles, Topological Methods in Differential Equations and Inclusions, Granas A. and Frigon M. (eds) NATO ASI Series C, Vol. 472, pp. 51–87. Kluwer Acad. Publ., Dordrecht (1995)
作者单位:Bashir Ahmad (1) Sotiris K. Ntouyas (1) (2)
1. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia 2. Department of Mathematics, University of Ioannina, 451 10, Ioannina, Greece
刊物类别:Mathematics and Statistics
刊物主题:Mathematics Computational Mathematics and Numerical Analysis Applied Mathematics and Computational Methods of Engineering Theory of Computation Mathematics of Computing
出版者:Springer Berlin / Heidelberg
ISSN:1865-2085
文摘
In this paper, we study a new class of Caputo type sequential fractional differential inclusions with nonlocal Riemann–Liouville fractional integral boundary conditions. The existence of solutions for the given problem is established for the cases of convex and non-convex multivalued maps by using standard fixed point theorems. The obtained results are well illustrated with the aid of examples. Keywords Fractional differential inclusions Sequential fractional derivative Integral boundary conditions Fixed point theorems