Boundary value problems of hybrid fractional integro-differential systems involving the conformable fractional derivative

Ala Eddine Taier; Ranchao Wu; Naveed Iqbal; Ala Eddine Taier; Ranchao Wu; Naveed Iqbal

doi:10.3934/math.20231339

AIMS Mathematics

2023, Volume 8, Issue 11: 26260-26274. doi: 10.3934/math.20231339

Previous Article Next Article

Research article

Boundary value problems of hybrid fractional integro-differential systems involving the conformable fractional derivative

1.
School of Mathematical Sciences, Anhui University, Hefei 230601, China
2.
Department of Mathematics, College of Science, University of Ha$ ' $il, Ha$ ' $il 2440, Saudi Arabia

Received: 17 March 2023 Revised: 28 May 2023 Accepted: 07 June 2023 Published: 13 September 2023
MSC : 26A33, 34A08, 34A12

In this paper, we study a boundary value problem for the hybrid fractional integro-differential system involving the conformable fractional derivative. We first discuss the existence of solutions using the Krasnoselskii fixed point theorem. The second result will be the existence and uniqueness of solution and we obtain it using the Banach fixed point theorem. Finally, we end our work with an example to illustrate our results.
- integro-differential system,
- conformable fractional derivative,
- fixed point theorem,
- existence and uniqueness
Citation: Ala Eddine Taier, Ranchao Wu, Naveed Iqbal. Boundary value problems of hybrid fractional integro-differential systems involving the conformable fractional derivative[J]. AIMS Mathematics, 2023, 8(11): 26260-26274. doi: 10.3934/math.20231339

Related Papers:

Abstract

In this paper, we study a boundary value problem for the hybrid fractional integro-differential system involving the conformable fractional derivative. We first discuss the existence of solutions using the Krasnoselskii fixed point theorem. The second result will be the existence and uniqueness of solution and we obtain it using the Banach fixed point theorem. Finally, we end our work with an example to illustrate our results.

References

[1]	S. H. Liang, J. H. Zhang, Existence of multiple positive solutions for m-point fractional boundary value problems on an infinite interval, Math. Comput. Model., 54 (2011), 1334–1346. https://doi.org/10.1016/j.mcm.2011.04.004 doi: 10.1016/j.mcm.2011.04.004
[2]	Z. B. Bai, W. C. Sun, Existence and multiplicity of positive solutions for singular fractional boundary value problems, Comput. Math. Appl., 63 (2012), 1369–1381. https://doi.org/10.1016/j.camwa.2011.12.078 doi: 10.1016/j.camwa.2011.12.078
[3]	R. P. Agarwal, D. O‘Regan, S. Stanek, Positive solutions for mixed problems of singular fractional differential equations, Math. Nachr., 285 (2012), 27–41. https://doi.org/10.1002/mana.201000043 doi: 10.1002/mana.201000043
[4]	J. R. Graef, L. Kong, Existence of positive solutions to a higher order singular boundary value problem with fractional q-derivatives, Fract. Calc. Appl. Anal., 16 (2013), 695–708. https://doi.org/10.2478/s13540-013-0044-5 doi: 10.2478/s13540-013-0044-5
[5]	D. O'Regan, S, Stanek, Fractional boundary value problems with singularities in space variables, Nonlinear Dynam., 71 (2013), 641–652. https://doi.org/10.1007/s11071-012-0443-x doi: 10.1007/s11071-012-0443-x
[6]	P. Thiramanus, S. K. Ntouyas, J. Tariboon, Existence and uniqueness results for Hadamard-type fractional differential equations with nonlocal fractional integral boundary conditions, Abstr. Appl. Anal., 2014 (2014), 902054. https://doi.org/10.1155/2014/902054 doi: 10.1155/2014/902054
[7]	J. Tariboon, S. K. Ntouyas, W. Sudsutad, Fractional integral problems for fractional differential equations via Caputo derivative, Adv. Differ. Equ., 181 (2014), 181. https://doi.org/10.1186/1687-1847-2014-181 doi: 10.1186/1687-1847-2014-181
[8]	B. Ahmad, S. K. Ntouyas, Nonlocal fractional boundary value problems with slit-strips boundary conditions, Fract. Calc. Appl. Anal., 18 (2015), 261–280. https://doi.org/10.1515/fca-2015-0017 doi: 10.1515/fca-2015-0017
[9]	J. Henderson, R. Luca, A. Tudorache, On a system of fractional differential equations with coupled integral boundary conditions, Fract. Calc. Appl. Anal., 18 (2015), 361–386. https://doi.org/10.1515/fca-2015-0024. doi: 10.1515/fca-2015-0024
[10]	T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57–66. https://doi.org/10.1016/j.cam.2014.10.016 doi: 10.1016/j.cam.2014.10.016
[11]	R. Khalil, M. A. Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65–70. https://doi.org/10.1016/j.cam.2014.01.002 doi: 10.1016/j.cam.2014.01.002
[12]	T. Bashiri, S. M. Vaezpour, C. Park, A coupled fixed point theorem and application to fractional hybrid differential problems, Fixed Point Theory Appl., 2016 (2016), 23. https://doi.org/10.1186/s13663-016-0511-x doi: 10.1186/s13663-016-0511-x
[13]	B. Ahmad, S. K. Ntouyas, A. Alsaedi, Existence results for a system of coupled hybrid fractional differential equations, Sci. World J., 2014 (2014), 426438. https://doi.org/10.1155/2014/426438 doi: 10.1155/2014/426438
[14]	S. Li, H. Yin, L. Li, The solution of cooperative fractional hybrid differential system, Appl. Math. Lett., 91 (2019), 48–54. https://doi.org/10.1016/j.aml.2018.11.008 doi: 10.1016/j.aml.2018.11.008
[15]	A. Yassine, J. Fahd, A. Thabet, On generalized fractional operators and a Gronwall type inequality with applications, Filomat, 31 (2017), 5457–5473. https://doi.org/10.2298/FIL1717457A doi: 10.2298/FIL1717457A
[16]	B. Ahmad, M. Alghanmi, A. Alsaedi, R. P. Agarwal, On an impulsive hybrid system of conformable fractional differential equations with boundary conditions, Int. J. Syst. Sci., 51 (2020), 958–970. https://doi.org/10.1080/00207721.2020.1746437 doi: 10.1080/00207721.2020.1746437
[17]	B. C. Dhage, S. K. Ntouyas, Existence results for boundary value problems for fractional hybrid differential inclusions, Topol. Method Nonlinear. Anal., 44 (2014), 229–238. https://doi.org/10.12775/TMNA.2014.044 doi: 10.12775/TMNA.2014.044
[18]	A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science, 2006.

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)