پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 610 |
| تعداد مقالات | 9,029 |
| تعداد مشاهده مقاله | 67,082,944 |
| تعداد دریافت فایل اصل مقاله | 7,656,400 |
On the hybrid fractional semilinear evolution equations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 25، دوره 16، شماره 1، فروردین 2025، صفحه 307-318 اصل مقاله (394.52 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28018.3781 | ||
| نویسندگان | ||
| Samira Zerbib* ؛ Khalid Hilal؛ Ahmed Kajouni | ||
| Laboratory LMACS, Sultan Moulay Slimane University, BP 523, Beni Mellal, 23000, Morocco | ||
| تاریخ دریافت: 14 مرداد 1401، تاریخ بازنگری: 31 خرداد 1402، تاریخ پذیرش: 03 تیر 1402 | ||
| چکیده | ||
| In this manuscript, we study the existence of mild solutions to initial value problems for hybrid fractional semi-linear evolution equations. On the other hand, we prove four different types of Ulam-Hyers stability results for mild solutions. The existence of mild solutions is proved by the Dhage fixed point theorem. Finally, an example is given to illustrate our results. | ||
| کلیدواژه‌ها | ||
| Hybrid fractional evolution equation؛ Mild solution؛ Ulam-Hyers stability؛ fixed point theorem | ||
| مراجع | ||
|
[1] P. Chen, Y. Li, Q. Chen, and R. Feng, On the initial value problem of fractional evolution equations with noncompact semigroup, Comput. Math. Appl. 67 (2014), no. 5, 1108–1115. [2] B.C. Dhage, On a fixed point theorem in Banach algebras with applications, Appl. Math. Lett. 18 (2005), no. 3, 273–280. [3] M. M. El-Borai, The fundamental solutions for fractional evolution equations of parabolic type, J. Appl. Math. Stoch. Anal. 2004 (2004), no. 3, 197–211. [4] M. M. El-Borai, On some fractional evolution equations with nonlocal conditions, Int. J. Pure Appl. Math. 24 (2005), no. 3, 405–413. [5] K. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, New York, 2000. [6] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Amsterdam, Elsevier Science B V, 2006. [7] F. Mainardi, On the initial value problem for the fractional diffusion-wave equation, Waves Stab. Contin. Media, World Scientific, Singapore, 1994, pp. 246–251. [8] F. Mainardi, P. Paraddisi, and R. Gorenflo, Probability distributions generated by fractional diffusion equations, J. Kertesz, I. Kondor (eds.) Econophysics: An Emerging Science. Kluwer Academic, Dordrecht, 2000. [9] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983. [10] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, vol. 198. Elsevier, Amsterdam, 1998. [11] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. [12] J. Sabatier, O.P. Agrawal, J.A.T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Dordrecht, Springer, 2007. [13] C.C. Travis and G.F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hung. 32 (1978), no. 1-2, 75–96. [14] Y. Zhou and F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl. 59 (2010), 1063–1077. [15] Y. Zhou and F. Jiao, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal.: Real World Appl. 11 (2010), no. 5, 4465–4475. | ||
|
آمار تعداد مشاهده مقاله: 387 تعداد دریافت فایل اصل مقاله: 222 |
||