On nonlinear neutral Liouville–Caputo-type fractional differential equations with Riemann–Liouville integral boundary conditions

References

[1] B. Ahmad, M. Alghanmi, A. Alsaedi, H. M. Srivastava and S. K. Ntouyas, The Langevin equation in terms of generalized Liouville–Caputo derivatives with nonlocal boundary conditions involving a generalized fractional integral, Mathematics 7 (2019), Article ID 533. 10.3390/math7060533Search in Google Scholar

[2] B. Ahmad and R. Luca, Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions, Appl. Math. Comput. 339 (2018), 516–534. 10.1016/j.amc.2018.07.025Search in Google Scholar

[3] B. Ahmad and S. K. Ntouyas, Some fractional-order one-dimensional semi-linear problems under nonlocal integral boundary conditions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 110 (2016), no. 1, 159–172. 10.1007/s13398-015-0228-4Search in Google Scholar

[4] B. Ahmad and S. K. Ntouyas, Boundary value problems of Hadamard-type fractional differential equations and inclusions with nonlocal conditions, Vietnam J. Math. 45 (2017), no. 3, 409–423. 10.1007/s10013-016-0213-zSearch in Google Scholar

[5] B. Ahmad, S. K. Ntouyas and J. Tariboon, Fractional differential equations with nonlocal integral and integer-fractional-order Neumann type boundary conditions, Mediterr. J. Math. 13 (2016), no. 5, 2365–2381. 10.1007/s00009-015-0629-9Search in Google Scholar

[6] A. Alsaedi, M. Alsulami, H. M. Srivastava, B. Ahmad and S. K. Ntouyas, Existence theory for nonlinear third-order ordinary differential equations with nonlocal multi-point and multi-strip boundary conditions, Symmetry 11 (2019), Article ID 281. 10.3390/sym11020281Search in Google Scholar

[7] A. Alsaedi, S. K. Ntouyas, R. P. Agarwal and B. Ahmad, On Caputo type sequential fractional differential equations with nonlocal integral boundary conditions, Adv. Difference Equ. 2015 (2015), Article ID 33. 10.1186/s13662-015-0379-9Search in Google Scholar

[8] K. Deimling, Multivalued Differential Equations, De Gruyter Ser. Nonlinear Anal. Appl. 1, Walter de Gruyter, Berlin, 1992. 10.1515/9783110874228Search in Google Scholar

[9] H. Fazli and J. J. Nieto, Fractional Langevin equation with anti-periodic boundary conditions, Chaos Solitons Fractals 114 (2018), 332–337. 10.1016/j.chaos.2018.07.009Search in Google Scholar

[10] J. R. Graef, L. Kong and M. Wang, Existence and uniqueness of solutions for a fractional boundary value problem on a graph, Fract. Calc. Appl. Anal. 17 (2014), no. 2, 499–510. 10.2478/s13540-014-0182-4Search in Google Scholar

[11] A. Granas and J. Dugundji, Fixed Point Theory, Springer Monogr. Math., Springer, New York, 2003. 10.1007/978-0-387-21593-8Search in Google Scholar

[12] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006. Search in Google Scholar

[13] M. Kisielewicz, Differential Inclusions and Optimal Control, Math. Appl. (East European Series) 44, Kluwer Academic, Dordrecht, 1991. Search in Google Scholar

[14] A. Lasota and Z. Opial, An application of the Kakutani—Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 781–786. Search in Google Scholar

[15] S. K. Ntouyas, S. Etemad and J. Tariboon, Existence of solutions for fractional differential inclusions with integral boundary conditions, Bound. Value Probl. 2015 (2015), Article ID 92. Search in Google Scholar

[16] S. K. Ntouyas, J. Tariboon and C. Thaiprayoon, Nonlocal boundary value problems for Riemann–Liouville fractional differential inclusions with Hadamard fractional integral boundary conditions, Taiwanese J. Math. 20 (2016), no. 1, 91–107. 10.11650/tjm.20.2016.5654Search in Google Scholar

[17] W. V. Petryshyn and P. M. Fitzpatrick, A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings, Trans. Amer. Math. Soc. 194 (1974), 1–25. 10.1090/S0002-9947-1974-2478129-5Search in Google Scholar

[18] J. Sabatier, O. P. Agrawal and J. A. T. Machado, Advances in Fractional Calculus, Springer, Dordrecht, 2007. 10.1007/978-1-4020-6042-7Search in Google Scholar

[19] B. N. Sadovskiĭ, On a fixed point principle, Funktsional. Anal. i Prilozhen. 1 (1967), no. 2, 74–76. 10.1007/BF01076087Search in Google Scholar

[20] E. Zeidler, Nonlinear Functional Analysis and its Applications: Fixed-point Theorems, Springer, New York, 1986. 10.1007/978-1-4612-4838-5Search in Google Scholar

[21] L. Zhang, B. Ahmad and G. Wang, Successive iterations for positive extremal solutions of nonlinear fractional differential equations on a half-line, Bull. Aust. Math. Soc. 91 (2015), no. 1, 116–128. 10.1017/S0004972714000550Search in Google Scholar