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Journal of Applied Mathematics and Computing

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24.11.2015 | Original Research

Existence of solutions for fractional differential equations with nonlocal and average type integral boundary conditions

verfasst von: Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2017

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Abstract

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions for a boundary value problem of fractional differential equations with nonlocal and average type integral boundary conditions. The Leray–Schauder nonlinear alternative, Krasnoselskii’s fixed point theorem and Banach’s fixed point theorem together with Hölder inequality are applied to construct proofs for the main results. Examples illustrating the obtained results are also presented.

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Zaslavsky, G.M.: Hamiltonian Chaos and Fractional Dynamics. Oxford University Press, Oxford (2005)MATH

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204, Elsevier Science, Amsterdam (2006)MATH

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)MATH

Konjik, S., Oparnica, L., Zorica, D.: Waves in viscoelastic media described by a linear fractional model. Integral Trans. Spec. Funct. 22, 283–291 (2011)MathSciNetCrossRefMATH

Yang, X.J., Hristov, J., Srivastava, H.M., Ahmad, B.: Modelling fractal waves on shallow water surfaces via local fractional Kortewegde Vries equation, Abstr. Appl. Anal., Article ID 278672, (2014)

Punzo, F., Terrone, G.: On the Cauchy problem for a general fractional porous medium equation with variable density. Nonlinear Anal. 98, 27–47 (2014)MathSciNetCrossRefMATH

Yang, X.J., Baleanu, D., Srivastava, H.M.: Local fractional similarity solution for the diffusion equation defined on Cantor sets. Appl. Math. Lett. 47, 54–60 (2015)MathSciNetCrossRefMATH

Webb, J.R.L., Infante, G.: Non-local boundary value problems of arbitrary order. J. Lond. Math. Soc. 79, 238–258 (2009)MathSciNetCrossRefMATH

Goodrich, C.: Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions. Comput. Math. Appl. 61, 191–202 (2011)MathSciNetCrossRefMATH

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)MathSciNetCrossRefMATH

11.

Cabada, A., Wang, G.: Positive solutions of nonlinear fractional differential equations with integral boundary value conditions. J. Math. Anal. Appl. 389, 403–411 (2012)MathSciNetCrossRefMATH

12.

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)MathSciNetCrossRefMATH

13.

Ahmad, B., Ntouyas, S.K.: Existence results for higher order fractional differential inclusions with multi-strip fractional integral boundary conditions. Electron. J. Qual. Theor. Differ. Equ. 9(20), 51–60 (2013)MathSciNetMATH

14.

O’Regan, D., Stanek, S.: Fractional boundary value problems with singularities in space variables. Nonlinear Dyn. 71, 641–652 (2013)MathSciNetCrossRefMATH

15.

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)MathSciNetCrossRefMATH

16.

Wang, G., Liu, S., Zhang, L.: Eigenvalue problem for nonlinear fractional differential equations with integral boundary conditions, Abstr. Appl. Anal., Article ID 916260, (2014)

17.

Liu, X., Liu, Z., Fu, X.: Relaxation in nonconvex optimal control problems described by fractional differential equations. J. Math. Anal. Appl. 409, 446–458 (2014)MathSciNetCrossRefMATH

18.

Bolojan-Nica, O., Infante, G., Precup, R.: Existence results for systems with coupled nonlocal initial conditions. Nonlinear Anal. 94, 231–242 (2014)MathSciNetCrossRefMATH

19.

Zhai, C., Xu, L.: Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter. Commun. Nonlinear Sci. Numer. Simul. 19, 2820–2827 (2014)MathSciNetCrossRef

20.

Yan, R., Sun, S., Lu, H., Zhao, Y.: Existence of solutions for fractional differential equations with integral boundary conditions. Adv. Differ. Equ. 2014, 25 (2014)MathSciNetCrossRefMATH

21.

Ahmad, B., Ntouyas, S.K., Alsaedi, A., Alzahrani, F.: New fractional-order multivalued problems with nonlocal nonlinear flux type integral boundary conditions. Bound. Value Probl. 2015, 83 (2015)MathSciNetCrossRefMATH

22.

Ahmad, B., Ntouyas, S.K.: On Hadamard fractional integro-differential boundary value problems. J. Appl. Math. Comput. 47, 119–131 (2015)MathSciNetCrossRefMATH

23.

Hu, L., Zhang, S., Shi, A.: Existence result for nonlinear fractional differential equation with \(p\)-Laplacian operator at resonance. J. Appl. Math. Comput. 48, 519–532 (2015)

24.

Foukrach, D., Moussaoui, T., Ntouyas, S.K.: Existence and uniqueness results for a class of BVPs for a nonlinear fractional differential equations depending on the fractional derivative. Georgian Math. J. 22(1), 45–55 (2015)CrossRefMATH

25.

Picone, M.: Su un problema al contorno nelle equazioni differenziali lineari ordinarie del secondo ordine. Ann. Scuola Norm. Super. Pisa Cl. Sci. 10, 1–95 (1908)MathSciNetMATH

26.

Whyburn, W.M.: Differential equations with general boundary conditions. Bull. Am. Math. Soc. 48, 692–704 (1942)MathSciNetCrossRefMATH

27.

Bitsadze, A., Samarskii, A.: On some simple generalizations of linear elliptic boundary problems. Russian Acad. Sci. Dokl. Math. 10, 398–400 (1969)MATH

28.

Ahmad, B., Alsaedi, A., Alghamdi, B.S.: Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions. Nonlinear Anal. Real World Appl. 9, 1727–1740 (2008)MathSciNetCrossRefMATH

29.

Čiegis, R., Bugajev, A.: Numerical approximation of one model of the bacterial self-organization. Nonlinear Anal. Model. Control 17, 253–270 (2012)MathSciNetMATH

30.

Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2005)MATH

31.

Krasnoselskii, M.A.: Two remarks on the method of successive approximations. Uspekhi Mat. Nauk. 10, 123–127 (1955)MathSciNet

Titel: Existence of solutions for fractional differential equations with nonlocal and average type integral boundary conditions
verfasst von: Bashir Ahmad
Sotiris K. Ntouyas
Ahmed Alsaedi
Publikationsdatum: 24.11.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2017
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-015-0960-0

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