On coupled snap system with integral boundary conditions in the $ \mathbb{G} $-Caputo sense

Sabri T. M. Thabet; Mohammed M. Matar; Mohammed Abdullah Salman; Mohammad Esmael Samei; Miguel Vivas-Cortez; Imed Kedim; Sabri T. M. Thabet; Mohammed M. Matar; Mohammed Abdullah Salman; Mohammad Esmael Samei; Miguel Vivas-Cortez; Imed Kedim

doi:10.3934/math.2023632

AIMS Mathematics

2023, Volume 8, Issue 6: 12576-12605. doi: 10.3934/math.2023632

Previous Article Next Article

Research article Special Issues

On coupled snap system with integral boundary conditions in the $ \mathbb{G} $-Caputo sense

1.
Department of Mathematics, University of Aden, Aden, Yemen
2.
Department of Mathematics, University of Lahej, Lahej, Yemen
3.
Department of Mathematics, Al-Azhar University-Gaza, Gaza Strip, Palestine
4.
Department of Mathematics and Statistics, Amran University, Amran, Yemen
5.
Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan 65178-38695, Iran
6.
Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Sede Quito, Ecuador
7.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Received: 06 December 2022 Revised: 19 January 2023 Accepted: 13 February 2023 Published: 28 March 2023
MSC : 34A08, 34B18

In this paper, we consider a coupled snap system in a fractional $ \mathbb{G} $-Caputo derivative sense with integral boundary conditions. Hyers-Ulam stability criterion is investigated, and a numerical simulation will be supplied to some applications. Some numerical simulations are presented to guarantee the theoretical results.
- snap problem,
- $ \mathbb{G} $-Caputo fractional differential equation,
- boundary value problem,
- Ulam-Hyers-Rassias stability
Citation: Sabri T. M. Thabet, Mohammed M. Matar, Mohammed Abdullah Salman, Mohammad Esmael Samei, Miguel Vivas-Cortez, Imed Kedim. On coupled snap system with integral boundary conditions in the $ \mathbb{G} $-Caputo sense[J]. AIMS Mathematics, 2023, 8(6): 12576-12605. doi: 10.3934/math.2023632

Related Papers:

Abstract

In this paper, we consider a coupled snap system in a fractional $ \mathbb{G} $-Caputo derivative sense with integral boundary conditions. Hyers-Ulam stability criterion is investigated, and a numerical simulation will be supplied to some applications. Some numerical simulations are presented to guarantee the theoretical results.

References

[1]	M. I. Abbas, M. Ghaderi, S. Rezapour, S. T. M. Thabet, On a coupled system of fractional differential equations via the generalized proportional fractional derivatives, J. Funct. Spaces, 2022 (2022), 4779213. https://doi.org/10.1155/2022/4779213 doi: 10.1155/2022/4779213
[2]	Y. Adjabi, M. E. Samei, M. M. Matar, J. Alzabut, Langevin differential equation in frame of ordinary and hadamard fractional derivatives under three point boundary conditions, AIMS Math., 6 (2021), 2796–2843. https://doi.org/10.3934/math.2021171 doi: 10.3934/math.2021171
[3]	H. Afshari, S. Kalantari, E. Karapinar, Solution of fractional differential equations via coupled fixed point, Electron. J. Differ. Equ., 2015 (2015), 1–12.
[4]	S. T. M. Thabet, B. Ahmad, R. P. Agarwal, On abstract Hilfer fractional integrodifferential equations with boundary conditions, Arab J. Math. Sci., 26 (2020), 107–125. https://doi.org/10.1016/j.ajmsc.2019.03.001 doi: 10.1016/j.ajmsc.2019.03.001
[5]	J. Alzabut, A. G. M. Selvam, R. A. El-Nabulsi, V. Dhakshinamoorthy, M. E. Samei, Asymptotic stability of nonlinear discrete fractional pantograph equations with non-local initial conditions, Symmetry, 13 (2021), 473. https://doi.org/10.3390/sym13030473 doi: 10.3390/sym13030473
[6]	P. Amiri, M. E. Samei, Existence of urysohn and atangana-baleanu fractional integral inclusion systems solutions via common fixed point of multi-valued operators, Chaos Solitons Fract., 165 (2022), 112822. https://doi.org/10.1016/j.chaos.2022.112822 doi: 10.1016/j.chaos.2022.112822
[7]	A. Boutiara, K. Guerbati, M. Benbachir, Caputo-Hadamard fractional differential equation with three-point boundary conditions in Banach spaces, AIMS Math., 5 (2020), 259–272. https://doi.org/10.3934/math.2020017 doi: 10.3934/math.2020017
[8]	J. V. d. C. Sousa, E. C. de Oliveira, On the Ulam-Hyers-Rassias stability for nonlinear fractional differential equations using the $\psi$-Hilfer operator, J. Fixed Point Theory Appl., 20 (2018), 96. https://doi.org/10.1007/s11784-018-0587-56 doi: 10.1007/s11784-018-0587-56
[9]	K. Deimling, Nonlinear functional analysis, Springer Berlin, Heidelberg, 1985. https://doi.org/10.1007/978-3-662-00547-7
[10]	A. R. Elsonbaty, A. M. El-Sayed, Further nonlinear dynamical analysis of simple jerk system with multiple attractors, Nonlinear Dyn., 87 (2017), 1169–1186. https://doi.org/10.1007/s11071-016-3108-3 doi: 10.1007/s11071-016-3108-3
[11]	H. P. W. Gottlieb, Harmonic balance approach to periodic solutions of nonlinear jerk equations, J. Sound Vib., 271 (2004), 671–683. https://doi.org/10.1016/S0022-460X(03)00299-2 doi: 10.1016/S0022-460X(03)00299-2
[12]	A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Vol. 204, North-Holland Mathematics Studies, Elsevier, 2006.
[13]	C. S. Liu, J. R. Chang, The periods and periodic solutions of nonlinear jerk equations solved by an iterative algorithm based on a shape function method, Appl. Math. Lett., 102 (2019), 106151. https://doi.org/10.1016/j.aml.2019.106151 doi: 10.1016/j.aml.2019.106151
[14]	N. Mahmudov, M. M. Matar, Existence of mild solution for hybrid differential equations with arbitrary fractional order, TWMS J. Pure Appl. Math., 8 (2017), 160–169.
[15]	M. M. Matar, Qualitative properties of solution for hybrid nonlinear fractional differential equations, Afr. Mat., 30 (2019), 1169–1179. https://doi.org/10.1007/s13370-019-00710-2 doi: 10.1007/s13370-019-00710-2
[16]	M. M. Matar, M. Jarad, M. Ahmad, A. Zada, S. Etemad, S. Rezapour, On the existence and stability of two positive solutions of a hybrid differential system of arbitrary fractional order via Avery-Anderson-Henderson criterion on cones, Adv. Differ. Equ., 2021 (2021), 423. https://doi.org/10.1186/s13662-021-03576-6 doi: 10.1186/s13662-021-03576-6
[17]	K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, New York: Wiley, 1993.
[18]	I. Podlubny, Fractional differential equations, New York: Academic Press, 1993.
[19]	M. S. Rahman, A. S. M. Z. Hasan, Modified harmonic balance method for the solution of nonlinear jerk equations, Results Phys., 8 (2018), 893–897. https://doi.org/10.1016/j.rinp.2018.01.030 doi: 10.1016/j.rinp.2018.01.030
[20]	S. Rezapour, M. E. Samei, On the existence of solutions for a multi-singular point-wise defined fractional $q$-integro-differential equation, Bound. Value Probl., 2020 (2020), 38. https://doi.org/10.1186/s13661-020-01342-3 doi: 10.1186/s13661-020-01342-3
[21]	S. Rezapour, S. T. M. Thabet, M. M. Matar, J. Alzabut, S. Etemad, Some existence and stability criteria to a generalized FBVP having fractional composite $p$-Laplacian operator, J. Funct. Spaces, 2021 (2021), 9554076. https://doi.org/10.1155/2021/9554076 doi: 10.1155/2021/9554076
[22]	M. E. Samei, V. Hedayati, S. Rezapour, Existence results for a fraction hybrid differential inclusion with Caputo-Hadamard type fractional derivative, Adv. Differ. Equ., 2019 (2019), 163. https://doi.org/10.1186/s13662-019-2090-8 doi: 10.1186/s13662-019-2090-8
[23]	M. E. Samei, M. M. Matar, S. Etemad, S. Rezapour, On the generalized fractional snap boundary problems via $G$-{C}aputo operators: existence and stability analysis, Adv. Differ. Equ., 2021 (2021), 498. https://doi.org/10.1186/s13662-021-03654-9 doi: 10.1186/s13662-021-03654-9
[24]	S. T. M. Thabet, M. B. Dhakne, On abstract fractional integro-differential equations via measure of noncompactness, Adv. Fixed Point Theory, 6 (2016), 175–193.
[25]	S. T. M. Thabet, M. B. Dhakne, On nonlinear fractional integro-differential equations with two boundary conditions, Adv. Stud. Contemp. Math., 26 (2016), 513–526.
[26]	S. T. M. Thabet, M. B. Dhakne, On positive solutions of higher order nonlinear fractional integro-differential equations with boundary conditions, Malaya J. Mat., 7 (2019), 20–26. https://doi.org/10.26637/MJM0701/0005 doi: 10.26637/MJM0701/0005
[27]	S. T. M. Thabet, M. B. Dhakne, M. A. Salman, R. Gubran, Generalized fractional Sturm-Liouville and langevin equations involving Caputo derivative with nonlocal conditions, Progr. Fract. Differ. Appl., 6 (2020), 225–237. https://doi.org/10.18576/pfda/060306 doi: 10.18576/pfda/060306
[28]	S. T. M. Thabet, S. Etemad, S. Rezapour, On a coupled Caputo conformable system of pantograph problems, Turk. J. Math., 45 (2021), 496–519. https://doi.org/10.3906/mat-2010-70 doi: 10.3906/mat-2010-70
[29]	C. Urs, Coupled fixed point theorems and applications to periodic boundary value problems, Miskolc Math. Notes, 14 (2013), 323–333. https://doi.org/10.18514/MMN.2013.598 doi: 10.18514/MMN.2013.598
[30]	H. Zhou, J. Alzabut, S. Rezapour, M. E. Samei, Uniform persistence and almost periodic solutions of a non-autonomous patch occupancy model, Adv. Differ. Equ., 2020 (2020), 143. https://doi.org/10.1186/s13662-020-02603-2 doi: 10.1186/s13662-020-02603-2

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)