پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 610 |
| تعداد مقالات | 9,026 |
| تعداد مشاهده مقاله | 67,082,732 |
| تعداد دریافت فایل اصل مقاله | 7,656,160 |
Qualitative properties of solutions of fractional order boundary value problems | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3427-3440 اصل مقاله (452.62 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22391.2457 | ||
| نویسندگان | ||
| A. M. A. El-Sayed1؛ H. H. G. Hashem2؛ Sh. M Al-Issa* 3، 4 | ||
| 1Faculty of Science, Alexandria University, Alexandria, Egypt | ||
| 2Department of Mathematics, College of Science, Qassim University, P.O. Box 6644 Buraidah 51452, Saudi Arabia | ||
| 3Department of Mathematics, Lebanese International University, Saida, Lebanon | ||
| 4Department of Mathematics, The International University of Beirut, Beirut, Lebanon | ||
| تاریخ دریافت: 10 فروردین 1400، تاریخ پذیرش: 07 خرداد 1400 | ||
| چکیده | ||
| In this article, we discuss two boundary value problems for fractional-order differential equations. We show unique solutions exist and some data continuous dependence, with aim of proving some characteristics for these solutions of a coupled system of conjugate orders. These coupled systems are equivalent to coupled systems of second-order differential equations. Therefore, the analysis of the spectra of these problems is a consequence of that of second-order differential equations. | ||
| کلیدواژه‌ها | ||
| Boundary value problem؛ Liouville-Caputo fractional derivative؛ Data continuous dependence؛ Eigenvalues and Eigenfunctions | ||
| مراجع | ||
|
[1] T.S. Aleroev, Boundary-Value Problems for Differential Equations with Fractional Derivatives, Dissert. on Doctoral Degree Phys.-Math. Sci., MGU, Moscow, 2000. [2] R.P. Agarwal, D. O’Regan and P.J.Y. Wong, Eigenvalues of a system of Fredholm integral equations, Math. Comput. Modell. 39 (2004) 1113–1150. [3] A. Cabada and G. Wang, Positive solutions of nonlinear fractional differential equations with integral boundary value conditions, J. Math. Anal. Appl. 389(1) (2012) 403–411. [4] D. Chalishajar and A. Kumar, Existence, uniqueness and Ulam’s stability of solutions for a coupled system of fractional differential equations with integral boundary conditions, Math. 6(6) (2018) 96. [5] A.M.A. El-Sayed and H.H.G. Hashem, Existence results for coupled systems of quadratic integral equations of fractional orders, Optim. Lett. 7(6) (2013) 1251–1260. [6] A.M.A. El-Sayed, H.H.G. Hashem and Sh M. Al-Issa, Characteristics of solutions of fractional hybrid integrodifferential equations in Banach algebra, Sahand Commun. Math. Anal. 18(3) (2020) 109–131. [7] A.M.A. El-Sayed and Sh M. Al-Issa, On a set-valued functional integral equation of Volterra-Stieltjes type, J. Math. Comput. Sci. 21(4) (2020) 273–285. [8] A.M.A. El-Sayed, Sh M. Al-Issa and N.M. Mawed, Results on solvability of nonlinear quadratic integral equations of fractional orders in Banach algebra, J. Nonlinear Sci. Appl. 14(4) (2021) 181–195. [9] K. Goebel and W.A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, 1990. [10] J. Henderson and R. Luca, Positive solutions for a system of coupled fractional boundary value problems, Lith. Math. J. 58(1) (2018) 15—32. [11] M. Jleli, D. O’Regan and B. Samet, Lyapunov-type inequalities for coupled systems of nonlinear fractional differential equations via a fixed point approach, J. Fixed Point Theory Appl. 21(2) (2019) 1–15. [12] A.N. Kolmogorov and S.V. Fomin, Introductory Real Analysis, Dover Publ. Inc., 1975. [13] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, North-Holland, 2006. [14] W. Kumam, M.B. Zada, K. Shah and R. A. Khan, Investigating a coupled Hybrid system of nonlinear fractional differential equations, Discrete Dyn. Nat. Soc. 2018 (2018) Article ID 5937572. [15] K. Shah, J. Wang, H. Khalil and R.A. Khan, Existence and numerical solutions of a coupled system of integral BVP for fractional differential equations, Adv. Difference Equ. 2018(1) (2018) 1–21. [16] A. Shidfara and A. Molabahrami, Solving a system of integral equations by an analytic method, Math. Comput. Modell. 54 (2011) 828-835. [17] G.T. Wang, S.Y. Liu and L.H. Zhang, Eigenvalue problem for nonlinear fractional differential equations with integral boundary conditions, Abstr. Appl. Anal. 2014 (2014) 916260. [18] C. Yujun and S. Jingxian, On existence of positive solutions of coupled integral boundary value problems for a nonlinear singular superlinear differential system, Electron. J. Qual. Theory Differential Equ. 41 (2012) 1–13. [19] A.Y. Al-Hossain, Eigenvalues for iterative systems of nonlinear Caputo fractional order three point boundary value problems, J. Appl. Math. Comput. 52 (2016) 157-172. [20] He. Ying, The eigenvalue problem for a coupled system of singular p-Laplacian differential equations involving fractional differential-integral conditions, Adv. Diff. Equ. 2016 (2016) 209. [21] X.G. Zhang, L.S. Liu, B. Wiwatanapataphee and YH. Wu, The eigenvalue for a class of singular p-Laplacian fractional differential equations involving the Riemann-Stieltjes integral boundary condition, Appl. Math. Comput. 235 (2014) 412–422. | ||
|
آمار تعداد مشاهده مقاله: 15,815 تعداد دریافت فایل اصل مقاله: 349 |
||