Nonlocal Neutral Functional Sequential Differential Equations with Conformable Fractional Derivative
Download PDF
Authors: N, CHEFNAJ, S. ZERBIB, K. HILAL AND A. KAJOUNI
DOI: 10.46793/KgJMat2606.871C
Abstract:
In this paper, we investigate the existence, uniqueness, and stability results of second-order neutral evolution differential equations within the framework of sequential conformable derivatives with nonlocal conditions. Utilizing Krasnoselskii’s fixed-point theorem, we establish results concerning the existence of at least one solution, while the uniqueness of the solution is derived using Banach’s fixed-point theorem. The final section is devoted to an example that illustrates the applicability of our findings.
Keywords:
Conformable derivative, cosine family of linear operators, fixed point theorem, nonlocal conditions.
References:
[1] K. Ezzinbi, F. Xianlong and K. Hilal, Existence and regularity in the α-norm for some neutral partial differential equations with nonlocal conditions, Nonlinear Anal. 67(5) (2007), 1613–1622. https://doi.org/10.1016/j.na.2006.08.003
[2] K. Hilal, A. Kajouni and N. Chefnaj, Existence of solution for a conformable fractional Cauchy problem with nonlocal condition, Int. J. Differ. Equ. 2022(1) (2022). https://doi.org/10.1155/2022/6468278
[3] M. E. Hernández, Existence of solutions to a second order partial differential equation with nonlocal conditions, Electron. J. Differ. Equ. 2003(51) (2003), 1–10.
[4] R. Khalil, M. Al-Horani, A. Yousef and 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
[5] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
[6] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
[7] W. E. Olmstead and C. A. Roberts, The one-dimensional heat equation with a nonlocal initial condition, Appl. Math. Lett. 10(3) (1997), 89–94. https://doi.org/10.1016/S0893-9659(97)00041-4
[8] M. I. A. Othman, S. M. Said and N. Sarker, Effect of hydrostatic initial stress on a fiber-reinforced thermoelastic medium with fractional derivative heat transfer, Multidiscipline Modeling in Materials and Structures 9(3) (2013), 410–426.
[9] M. I. A. Othman, N. Sarkar and S. Y. Atwa, Effect of fractional parameter on plane waves of generalized magneto-thermoelastic diffusion with reference temperature-dependent elastic medium, Comput. Math. Appl. 65(7) (2013), 1103–1118. https://doi.org/10.1016/j.camwa.2013.01.047
[10] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
[11] S. M. Said, E. M. Abd-Elaziz and M. I. A. Othman, Effect of gravity and initial stress on a nonlocal thermo-viscoelastic medium with two-temperature and fractional derivative heat transfer, ZAMM Z. Angew. Math. Mech. 102(7) (2022), Article ID e202100316. https://doi.org/10.1002/zamm.202100316
[12] S. M. Said, M. I. A. Othman and M. G. Eldemerdash, A novel model on nonlocal thermoelastic rotating porous medium with memory-dependent derivative, Multidiscipline Modeling in Materials and Structures 18(5) (2022), 793–807. https://doi.org/10.1108/MMMS-05-2022-0085
[13] N. Sarkar, S. Mondal and M. I. A. Othman, L-S theory for the propagation of the photo-thermal waves in a semiconducting nonlocal elastic medium, Waves in Random and Complex Media 32(6) (2022), 2622–2635. https://doi.org/10.1080/17455030.2020.1859161
[14] S. Shaw and M. I. A. Othman, On the concept of a conformable fractional differential equation, Journal of Engineering and Thermal Sciences 1(1) (2021), 17–29. https://doi.org/10.21595/jets.2021.22072
[15] X. B. Shu and Q. Wang, The existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1 < α < 2, Comput. Math. Appl. 64(6) (2012), 2100–2110. https://doi.org/10.1016/j.camwa.2012.04.006
[16] C. C. Travis and G. F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Hungar. 32(2) (1978), 75–96.
Login:
