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A nonlocal boundary value problems for hybrid ϕ-Caputo fractional integro-differential equations

1 College of Science, Tianjin University of Technology, Tianjin 300384, China
2 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Special Issues: Nonlinear Differential Equations and Applications

In this paper, we discuss the existence of solutions for a nonlocal boundary value problems for hybrid ϕ-Caputo fractional integro-differential equations. Our main result is based on a hybrid fixed point theorem due to Dhage. Finally, we give an example to illustrate our main result.
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References

1. B. C. Dhage, V. Lakshmikantham, Basic results on hybrid differential equation, Nonlinear Anal. Hybrid Syst., 4 (2010), 414-424.    

2. Y. Zhao, S. Sun, Z. Han, et al. Theory of fractional hybrid differential equations, Comput. Math. Appl., 62 (2011), 1312-1324.    

3. S. Sun, Y. Zhao, Z. Han, et al. The existence of solutions for boundary value problem of fractional hybrid differential equations, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 4961-4967.    

4. B. Ahmad, S. K. Ntouyas, An existence theorem for fractional hybrid differential inclusions of Hadamard type with Dirichlet boundary conditions, Abstr. Appl. Anal., 2014 (2014), 705809.

5. B. C. Dhage, S. K. Ntouyas, Existence results for boundary value problems for fractional hybrid differential inclusions, Topol. Methods Nonlinar Anal., 44 (2014), 229-238.

6. B. Ahmad, S. K. Ntouyas, A. Alsaedi, Existence results for a system of coupled hybrid fractional differential equations, Sci. World J., 2014 (2014), 426438.

7. K. Hilal, A. Kajouni, Boundary value problems for hybrid differential equations with fractional order, Adv. Differ. Equ., 2015 (2015), 183.

8. B. Ahmad, S. K. Ntouyas, J. Tariboon, A nonlocal hybrid boundary value problem of Caputo fractional integro-differential equations, Acta Math. Sci., 36 (2016), 1631-1640.    

9. Z. Ullah, A. Ali, R. A. Khan, et al. Existence results to a class of hybrid fractional differential equations, Matriks Sains Mat. (MSMK), 1 (2018), 13-17.

10. M. E. Samei, V. Hedayati, S. Rezapour, Existence results for a fractional hybrid differential inclusion with Caputo-Hadamard type fractional derivative, Adv. Differ. Equ., 2019 (2019), 163.

11. Z. Baitiche, K. Guerbati, M. Benchohra, et al. Boundary value problems for Hybrid Caputo fractional differential equations, Mathematics, 7 (2019), 1-11.

12. K. Zhang, J. Wang, W. Ma, Solutions for integral boundary value problems of nonlinear Hadamard fractional differential equations, J. Funct. Space., 2018 (2018), 1-10.

13. J. Jiang, D. O'Regan, J. Xu, et al. Positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions, J. Inequal. Appl., 2019 (2019), 1-18.    

14. J. Wang, Y. Zhang, On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives, Appl. Math. Lett., 39 (2015), 85-90.    

15. K. Zhang, Z. Fu, Solutions for a class of Hadamard fractional boundary value problems with signchanging nonlinearity, J. Funct. Space., 2019 (2019), 1-7.

16. S. NageswaraRao, M. Singh, M. Z. Meetei, Multiplicity of positive solutions for Hadamard fractional differential equations with p-Laplacian operator, Bound. Value Probl., 2020 (2020), 1-25.    

17. Z. Baitiche, C. Derbazi, On the solvability of a fractional hybrid differential equation of hadamard type with dirichlet boundary conditions in Banach algebras, Commun. Optim. Theory, 2020 (2020), 9.

18. M. Jamil, R. A. Khan, K. Shah, Existence theory to a class of boundary value problems of hybrid fractional sequential integro-differential equations, Bound. Value Probl., 2019 (2019), 77.

19. R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci. Numer. Simulat., 44 (2017), 460-481.    

20. R. Almeida, A. B. Malinowska, T. Odzijewicz, On systems of fractional differential equations with the ψ-Caputo derivative and their applications, Math. Methods Appl. Sci., 2019. Available from: http://doi.org/10.1002/mma.5678.

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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