References
- P. Agarwal, J. Choi and R.B. Paris. Extended Riemann-Liouville fractional derivative operator and its applications. J. Nonlinear Sci. Appl., 8:451–466, 2015.
- B. Ahmad, A. Alsaedi and B.S. Alghamdi. Analytic approximation of solutions of the forced duffing equation with integral boundary conditions. Nonlinear Anal. Real World Appl., 9(4):1727–1740, 2008. https://doi.org/10.1016/j.nonrwa.2007.05.005.
- B. Ahmad and J. Nieto. Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions. Bound. Value Probl., 2011:36, 2011. https://doi.org/10.1186/1687-2770-2011-36.
- B. Ahmad and S.K. Ntouyas. Nonlocal fractional boundary value problems with slit-strips integral boundary conditions. Fract. Calc. Appl. Anal., 18(1):261–280, 2015. https://doi.org/10.1515/fca-2015-0017.
- B. Ahmad, S.K. Ntouyas and A. Alsaedi. A study of nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type multistrip boundary conditions. Math. Probl. Eng., Art. ID 320415:9 pp, 2013.
- B. Ahmad, S.K. Ntouyas and J. Tariboon. A study of mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions via endpoint theory. Appl. Math. Lett., 52:9–14, 2016. https://doi.org/10.1016/j.aml.2015.08.002.
- Z.B. Bai and W. Sun. Existence and multiplicity of positive solutions for singular fractional boundary value problems. Comput. Math. Appl., 63(9):1369–1381, 2012. https://doi.org/10.1016/j.camwa.2011.12.078.
- D.W. Boyd and J.S.W. Wong. On nonlinear contractions. Proc. Amer. Math. Soc., 20:458–464, 1969. https://doi.org/10.1090/S0002-9939-1969-0239559-9.
- A.G. Butkovskii, S.S. Postnov and E.A. Postnova. Fractional integro-differential calculus and its control-theoretical applications in mathematical fundamentals and the problem of interpretation. Automation and Remote Control, 74(4):543–574, 2013. https://doi.org/10.1134/S0005117913040012.
- J. Choi, D. Ritelli and P. Agarwal. Some new inequalities involving generalized Erdélyi-Kober fractional q-integral operator. Applied Mathematical Sciences, 9(72):3577–3591, 2015. https://doi.org/10.12988/ams.2015.53190.
- A. Erdélyi and H. Kober. Some remarks on hankel transforms. Quart. J. Math., Oxford, Second Ser., 11(1):212–221, 1940. https://doi.org/10.1093/qmath/os-11.1.212.
- C. Goodrich. Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions. Comput. Math. Appl., 61(2):191–202, 2011. https://doi.org/10.1016/j.camwa.2010.10.041.
- J.R. Graef, J. Henderson and A. Ouahab. Fractional differential inclusions in the almgren sense. Fract. Calc. Appl. Anal., 18:673–686, 2015. https://doi.org/10.1515/fca-2015-0041.
- A. Granas and J. Dugundji. Fixed Point Theory. Springer-Verlag, New York, 2003. https://doi.org/10.1007/978-0-387-21593-8.
- U.N. Katugampola. New approach to a generalized fractional integral. Appl. Math. Comput., 218(3):860–865, 2011. https://doi.org/10.1016/j.amc.2011.03.062.
- A.A. Kilbas, H.M. Srivastava and J.J. Trujillo. Theory and Applications of Fractional Differential Equations. Elsevier Science B.V., N Amsterdam, 2006.
- V. Kiryakova. Generalized Fractional Calculus and Applications. Pitman Research Notes in Math. 301, Longman, Harlow - J. Wiley, N. York, 1994.
- J. Klafter, S.C. Lim and R. Metzler. Fractional Dynamics in Physics. World Scientific, Singapore, 2011.
- H. Kober. On fractional integrals and derivatives. Quart. J. Math. Oxford, 9:193–211, 1940. https://doi.org/10.1093/qmath/os-11.1.193.
- M.A. Krasnoselskii. Two remarks on the method of successive approximations. Uspekhi Mat. Nauk, 10:123–127, 1955.
- X. Liu, M. Jia and W. Ge. Multiple solutions of a p-Laplacian model involving a fractional derivative. Adv. Difference Equ., 2013:126, 2013. https://doi.org/10.1186/1687-1847-2013-126.
- Y. Liu. Multiple positive solutions of bvps for singular fractional differential equations with non-caratheodory nonlinearities. Math. Model. Anal., 19(3):395–416, 2014. https://doi.org/10.3846/13926292.2014.925984.
- A.B. Malinowska, T. Odzijewicz and D.F.M. Torres. Advanced Methods in the Fractional Calculus of Variations. Springer-Verlag, New York, 2015. https://doi.org/10.1007/978-3-319-14756-7.
- S.K. Ntouyas, S. Etemad and J. Tariboon. Existence results for multiterm fractional differential inclusions. Adv. Difference Equ., 2015:140, 2015. https://doi.org/10.1186/s13662-015-0481-z.
- D. O’Regan and S. Stanek. Fractional boundary value problems with singularities in space variables. Nonlinear Dynam., 71(4):641–652., 2013. https://doi.org/10.1007/s11071-012-0443-x.
- J. Sabatier, O.P. Agrawal and J.A.T. Machado. Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht, 2007. https://doi.org/10.1007/978-1-4020-6042-7.
- S.G. Samko, A.A. Kilbas and O.I. Marichev. On fractional integrals and derivatives Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, New York, 1993.
- D.R. Smart. Fixed Point Theorems. Cambridge University Press, 1980.
- I.N. Sneddon. The use in mathematical analysis of Erdélyi-Kober operators and some of their applications. In H. Ammann and V.A. Solonnikov(Eds.), Fractional Calculus and Its Applications, Proc. Internat. Conf. Held in New Haven, Lecture Notes in Math. 457, pp. 37–79. Springer, N. York, 1975.
- J. Tariboon, S.K. Ntouyas and A. Singubol. Boundary value problems for fractional differential equations with fractional multi-term integral conditions. J. App. Math., Art. ID 806156:10 pp., 2014.
- P. Thiramanus, S.K. Ntouyas and J. Tariboon. Existence and uniqueness results for Hadamard-type fractional differential equations with nonlocal fractional integral boundary conditions. Abstr. Appl. Anal., Art. ID 902054:9 pp., 2014.
- N. Thongsalee, S.K. Ntouyas and J. Tariboon. Nonlinear Riemann-Liouville fractional differential equations with nonlocal Erdélyi-Kober fractional integral conditions. Frac. Calc. Appl. Anal., 19:480–497, 2016. https://doi.org/10.1515/fca-2016-0025.
- R. Čiegis and A. Bugajev. Numerical approximation of one model of the bacterial self-organization. Nonlinear Anal. Model. Control, 17(3):253–270, 2012.
- X. Zhang, P. Agarwal, Z. Liu and H. Peng. The general solution for impulsive differential equations with Riemann Liouville fractional-order q ∈ (1, 2). Open Math., 13(1):908–930, 2015. https://doi.org/10.1515/math-2015-0073.