پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 628 |
| تعداد مقالات | 9,179 |
| تعداد مشاهده مقاله | 67,526,947 |
| تعداد دریافت فایل اصل مقاله | 8,061,655 |
Nonlinear fractional differential equations with advanced arguments | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 1413-1423 اصل مقاله (380.36 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.13473.1697 | ||
| نویسندگان | ||
| Bakr H Rizqan* 1؛ Dnyanoba Dhaigude2 | ||
| 1Department of Mathematics, Faculty of Education, Applied Sciences and Arts, Amran University, Amran, Yemen | ||
| 2Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad - 431004, India | ||
| تاریخ دریافت: 30 آذر 1396، تاریخ پذیرش: 07 مهر 1399 | ||
| چکیده | ||
| In this paper, we develop the existence and uniqueness theory of fractional differential equation involving Riemann-Liouville differential operator of order $0 < \alpha< 1$, with advanced argument and integral boundary conditions. We investigate the uniqueness of the solution by using Banach fixed point theorem, we apply the comparison result to obtain the existence and uniqueness of solution by monotone iterative technique also by using weakly coupled extremal solution for the nonlinear boundary value problem (BVP). As an application of this technique, existence and uniqueness results are obtained. | ||
| کلیدواژه‌ها | ||
| Fractional di¤erential equations with advanced argument؛ Riemann-Liouville fractional derivatives؛ existence and uniqueness؛ monotone iterative technique؛ lower and upper solution؛ integral boundary condition | ||
| مراجع | ||
|
[1] P. Chen, X. Zhang and Y. Li, Study on fractional non-autonomous evolution equations with delay, Compu. Math. Appl. 73 (2017) 794–803. [2] J.V. Devi, F.A. McRae and Z. Drici, Variational Lyapunov method for fractional differential equations, Comp. Math. Appl. 64 (2012) 2982–2989. [3] D.B. Dhaigude and B.H. Rizqan, Existence and uniqueness of solutions for fractional differential equations with advanced arguments, Adv. Math. Mod. Appl. 2 (2017) 240–250. [4] D.B. Dhaigude and B.H. Rizqan, Monotone iterative technique for Caputo fractional differential equations with deviating arguments, Ann. Pure Appl. Math. 16 (2018) 181–191. [5] D.B. Dhaigude and B.H. Rizqan, Existence results for nonlinear fractional differential equations with deviating arguments under integral boundary conditions, Far East J. Math. Sci. 108 (2018) 273–284. [6] D.B. Dhaigude and B.H. Rizqan, Existence and uniqueness of solutions of fractional differential equations with deviating arguments under integral boundary conditions, Kyungpook Math. J. 59 (2019) 191–202. [7] T. Jankowski, Fractional differential equations with deviating arguments, Dyn. Syst. Appl. 17 (2008) 677–684. [8] T. Jankowski, Fractional problems with advanced arguments, Appl. Math. Comput. 230 (2014) 371–382. [9] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Thesssory and Applications of Fractional Differential Equations, In: North-Holland Mathematics Studies, vol. 204. Elsevier Science B.V. Amsterdam, 2006. [10] V. Lakshmikanthan and A.S. Vatsala, General uniqueness and monotone iterative technique for fractional differential equations, Appl. Math. Lett. 21 (2008) 828–834. [11] L. Lin, X. Liu and H. Fang, Method of upper and lower solutions for fractional differential equations, Electron. J. Diff. Eq. 100 (2012) 1–13. [12] F.A. McRae, Monotone iterative technique and existence results for fractional differential equations, Nonlinear Anal. 71 (2009) 6093–6096. [13] J.A. Nanware and D. B. Dhaigude, Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions, J. Nonlinear Sci. Appl. 7 (2014) 246–254. [14] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York, 1999. [15] B.H. Rizqan and D.B. Dhaigude, Positive solutions of nonlinear fractional differential equations with advanced arguments under integral boundary value conditions, Indian J. Math. 60 (2018) 491–507. [16] B.H. Rizqan and D.B. Dhaigude, Nonlinear boundary value problem of fractional differential equations with advanced arguments under integral boundary conditions, Tamkang J. Math. 51 (2020) 101–112. [17] Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore, 2014. | ||
|
آمار تعداد مشاهده مقاله: 15,683 تعداد دریافت فایل اصل مقاله: 429 |
||