On solutions of the nonlocal generalized coupled systems beam-type and travelling waves
Yacine Boulatioury.boulatiour@univ-chlef.dzDepartment of MathematicsFaculty of the Exact Sciences and ComputerLaboratory of Mathematics and ApplicationsUniversity of Hassiba BenboualiChlef, 02000, Algeria0009-0004-0296-0440View full profile → , Amina Boucennaamina.boucenna@g.ens-kouba.dzDepartment of MathematicsLaboratory of Fixed Point Theory and Applications, École Normale Supérieure, ENS, KoubaKouba (Algiers), 16308, Algeria0009-0006-9772-2799View full profile → , Souad Ayadisouad.ayadi@univ-dbkm.dzDepartment of PhysicsFaculty of Material Sciences and Computer ScienceAcoustics and Civil Engineering Laboratory, Thniet El Had StreetKhemis Miliana UniversityKhemis, Miliana, 44225, Algeria0000-0001-7011-5389View full profile → , *Abdelkader BenaliCorresponding authorbenali4848@gmail.comDepartment of MathematicsFaculty of the Exact Sciences and ComputerLaboratory of Mathematics and ApplicationsUniversity of Hassiba BenboualiChlef, 02000, Algeria0000-0001-6205-3499View full profile →
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- Received:
- 01 Oct 2025
- Published Online:
- 02 Jun 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2513
- Pages:
- 1–21
Abstract
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References
[1] A. Abdelnebi and Z. Dahmani, “New van der Pol-Duffing jerk fractional differential oscillator of sequential type,” Mathematics, vol. 10, pp. 35-46 (2022).
[2] A. Anber, Z. Dahmani, Y. Gouari, and R. W. Ibrahim, “A generalized system of fractional differential equations of beam type: Existence of solutions and stability,” Applied Mathematics E-Notes, vol. 24, pp. 540-557 (2024).
[3] A. Alsaedi, S. K. Ntouyas, and B. Ahmad, “Existence results for fractional integrodifferential equations with nonlocal integral boundary conditions,” Abstract and Applied Analysis, vol. 2015, pp. 1-10, Art. no. 205452 (2015).
[4] E. A. Algehyne, N. H. Altaweel, M. Areshi, and F. A. Khan, “Relation-theoretic almost ϕ-contractions with an application to elastic beam equations,” AIMS Mathematics, vol. 8, no. 8, pp. 18919-18929 (2023).
[5] A. Chouraqui, Z. Dahmani, and Y. Gouari, “Solvability of a fractional differential problem for beam equilibrium,” Fractional Differential Calculus, vol. 14, no. 2, pp. 273-293 (2024).
[6] I. Bachar, H. Eltayeb, and S. Mesloub, “Existence results for a class of fractional differential beam type equations,” Axioms, vol. 12, no. 10, p. 939 (2023).
[7] I. M. Batiha, S. Alshorm, I. H. Jebril, and M. A. Hammad, “A brief review about fractional calculus,” Journal of Open Problems in Computational Mathematics, vol. 15, no. 4, pp. 39-56 (2022).
[8] K. Bensaassa, Z. Dahmani, M. Rakah, and M. Z. Sarikaya, “Beam deflection coupled systems of fractional differential equations: existence of solutions, Ulam-Hyers stability and travelling waves,” Analysis and Mathematical Physics, vol. 14 (2024).
[9] K. Bensaassa, R. Wael Ibrahim, and Z. Dahmani, “Existence, uniqueness and numerical simulation for solutions of a class of fractional differential problems,” submitted for publication.
[10] M. Benbachir, “Convex fractional derivative,” *preprint*. [Online]. Available: DOI: 10.13140/RG.2.2.29093.97764
[11] Z. Dahmani, M. A. Abdellaoui, and M. Houas, “Coupled systems of fractional integro-differential equations involving several functions,” Theory and Applications of Mathematics & Computer Science, vol. 5, no. 1 (2015).
[12] Z. Dahmani, A. Anber, and I. Jebril, “Solving conformable evolution equations by an extended numerical method,” Jordan Journal of Mathematics and Statistics (JJMS), vol. 15, no. 2, pp. 363-380 (2022).
[13] C. P. Gupta, “Existence and uniqueness theorems for the bending of an elastic beam equation,” Applicable Analysis, vol. 26, no. 4, pp. 289-304 (1988).
[14] Y. Gouari and Z. Dahmani, “Stability of solutions for two classes of fractional differential equations of Lane-Emden type,” Journal of Interdisciplinary Mathematics, vol. 24, no. 8, pp. 2087-2099 (2021).
[15] M. Houas and Z. Dahmani, “On existence of solutions for fractional differential equations with nonlocal multipoint boundary conditions,” Lobachevskii Journal of Mathematics, vol. 37, no. 2, pp. 120-127 (2016).
[16] D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the U.S.A., vol. 27, no. 4, pp. 222-224 (1941).
[17] R. W. Ibrahim, “Stability of a fractional differential equation,” International Journal of Mathematical and Computational Sciences, vol. 7, no. 3, pp. 487-492 (2013).
[18] C. Intartaglia, L. Soria, and M. Porfiri, “Hydrodynamic coupling of two sharp-edged beams vibrating in a viscous fluid,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 470, Art. no. 20130397 (2014).
[19] G. Jumarie, “Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results,” Computers & Mathematics with Applications, vol. 51, no. 9-10, pp. 1367-1376 (2006).
[20] R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, “A new definition of fractional derivative,” Journal of Computational and Applied Mathematics, vol. 264, pp. 65-70 (2014).
[21] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations. Amsterdam, The Netherlands: Elsevier B. V. (2006).
[22] Y. Liu, “Existence and non-existence of positive solutions of BVPs for fractional order elastic beam equations with a non-Caratheodory nonlinearity,” Applied Mathematical Modelling, vol. 38, no. 2, pp. 620-640 (2014).
[23] W. Malfliet, “The tanh method: Exact solutions of nonlinear evolution and wave equations,” Physica Scripta, vol. 54, no. 6, pp. 563-568 (1996).
[24] M. Marin, A. Ochsner, and M. M. Bhatt, “Some results in Moore-Gibson-Thompson thermoelasticity of dipolar bodies,” ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, vol. 100, no. 12, Art. no. e202000090 (2020).
[25] K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations. New York, NY, USA: Wiley (1993).
[26] H. Mohamed, “Sequential fractional pantograph differential equations with nonlocal boundary conditions: uniqueness and Ulam-Hyers-Rassias stability,” Results in Nonlinear Analysis, vol. 5, no. 1, pp. 29-41 (2022).
[27] J. V. Morales, L. Rodríguez-Esparza, and M. R. Aranda, “Deflection of beams modeled by fractional differential equations,” Fractal and Fractional, vol. 6, no. 11, p. 626 (2022).
[28] I. Podlubny, Fractional Differential Equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Mathematics in Science and Engineering, vol. 198). San Diego, CA, USA: Academic Press (1999).
[29] M. Rakah, Z. Dahmani, and A. Senouci, “New uniqueness results for fractional differential equations with a Caputo and Khalil derivatives,” Applied Mathematics & Information Sciences, vol. 16, no. 6, pp. 943-952 (2022).
[30] E. Zeidler, Nonlinear Functional Analysis and its Applications. I. Fixed-point Theorems. New York, NY, USA: Springer-Verlag (1986).




