Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem

Alsadi, Wadhah Ahmed; Hussein, Mokhtar; Abdullah, Tariq Q. S.

doi:10.22034/cmde.2021.32807.1580

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

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	Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem
Computational Methods for Differential Equations
مقاله 8، دوره 9، شماره 4، دی 2021، صفحه 1042-1058 اصل مقاله (169.08 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.32807.1580
نویسندگان
Wadhah Ahmed Alsadi ¹؛ Mokhtar Hussein²؛ Tariq Q. S. Abdullah³
¹School of Mathematics and Physics, China University of Geosciences(Wuhan), Wuhan, China
²School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China.
³School of Mathematics and Physics, China University of Geosciences(Wuhan), Wuhan, China.
چکیده
In this literature, we study the existence and stability of the solution of the boundary value problem of fractional differential equations with Φp-Laplacian operator. Our problem is based on Caputo fractional derivative of orders σ, ϵ, where k − 1 < σ, ϵ ≤ k, and k ≥ 3. By using the Schauder fixed point theory and properties of the Green function, some conditions are established which show the criterion of the existence and non-existence solution for the proposed problem. We also investigate some adequate conditions for the Hyers-Ulam stability of the solution. Illustrated examples are given as an application of our result.
کلیدواژه‌ها
Fractional differential equations(FDEs)؛ Caputo factional derivative؛ Boundary value problem(BVP)؛ Schauder fixed point؛ Hyers-Ulams(UH) stability؛ Existence and uniqueness(EUS)؛ Laplacian operator؛ Differential equations(DEs)

مراجع
[1] B. Ahmad and J. J. Nieto, Existence of solutions for nonlocal boundary value problems of higherorder nonlinear fractional differential equations, Abstr. Appl. anal, 1(2009),1–9. [2] G. A. Anastassiou, On right fractional calculus, Chaos, Solitons and fractals, 42(2009), 365–376. [3] A. Alkhazzan, P. Jiang, D. Baleanu, H. Khan, and A. Khan, Stability and existence results for a class of nonlinear fractional differential equations with singularity, Math Meth Appl Sci, 41(18) (2018), 1-14. [4] B. Ahmad and J. J. Nieto, Existence results for a coupled system of nonlinear fractional differen- tial equations with three point boundary conditions, Comput. Math. Appl, 58 (2009), 1838–1843. [5] W. Al-Sadi, H. Zhenyou, and A. Alkhazzan, Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity, J Taibah Univ Sci, 13 (2019), 951–960. [6] M. Benchohra, J. R. Graef, and S. Hamani, Existence results for boundary value problems with nonlinear fractional differential equations, Appl. Anal, 87 (2008), 851–863. [7] G. Chai, Positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator. Bound. Value. Probl, 1 (2012), 1–20. [8] X. Dou, Y. Li, and P. Liu, Existence of solutions for a four point boundary value problem of a nonlinear fractional differential equation, Op. Math, 31 (2011), 359–372. [9] MH. Derakhshan, A. Ansari, and M. Ahmadi Darani, On asymptotic stability of Weber frac- tional differential systems, Comput. Methods Differ.Equ, 6(1) (2018), 30–9. [10] M. El-Shahed, On the existence of positive solutions for a boundary value problem of fractional order, Thai J. Math, 5 (2007), 143–150. [11] D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Orlando, 5 (1988). [12] C. S. Goodrich, Existence and uniqueness of solutions to a fractional difference equation with non-local conditions, Comput. Math. Appl, 61 (2011), 191–202. [13] M. Gurbuz and M. Tezer-Sezgin, Numerical stability of rbf approximation for unsteady mhd flow equations, 2 (2019), 123–134. [14] R. Hilfer, Application of fractional calculus in physics, World. scientic, 2000. [15] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differ- ential equations, Elsevier, 204 (2006). https://doi.org/10.1155/2009/494720. [16] R. A. Khan and M. Rehman, Existence of Multiple Positive Solutions for a General System of Fractional Dierential Equations, Commun. Appl. Nonlinear Anal, 18 (2011), 25–35. [17] R. A. Khan, M. Rehman, and N. Asif, Three point boundary value problems for nonlinear fractional differential equations, Acta. Math. Sci, 31(4) (2011), 1–10. [18] H. Khan, R. Khan, and M. Alipour,On existence and uniqueness of solution for fractional boundary value problem, j. fractional calc. & appl. , Lecture Notes in Mathematics, 6(1) (2015). [19] H. Khan, W. Chen, and H. Sun, Analysis of positive solution and Hyers-Ulam stability for a class of singular fractional differential equations with p-Laplacian in Banach space, Math Method Appl Sci , 41(9), (2018), 3430–3440. [20] V. V. Kharat and S. R. Tate, Ulam stabilities for a class of nonlinear mixed fractional integro– differential equations, Nonlin Stud, 27(3) (2020), 811–821. [21] J. A. L´opez-Renter´ıa and B. Aguirre-Hernandez and G, Lmi stability test for fractional order initialized control systems, Appl and Comput Mathematics, 18(2019), 50–61. [22] RL. Magin, Fractional calculus in bioengineering, part 1, Critical Reviews in Biomedical Engi- neering, 32 (2004). [23] K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, Wiley, 1993. [24] K. B. Oldhalm and J. Spainer, The fractional calculus, Academic Press, New York, 1974. [25] K.B. Oldham, Fractional differential equations in electrochemistry, Adv Eng Soft, 41 (2010), 9–12. [26] I. Podlubny, Fractional dierential equations, Academic Press, New York, 1999. [27] M. Rehman, R. A. Khan, and J. Henderson, Existence and uniqueness of solutions for nonlinear fractional differential equations with integral boundary conditions, Fract. Dyn.Syst, 1 (2011), 29–43. [28] J. Sabatier, O. P. Agrawal, and J. A. Tenreiro and Machado, Advances in Fractional Calculus, Springer, 4(9) (2007). [29] X. Su, Boundary value problem for a coupled system of nonlinear fractional differential equa- tions, Appl. Math. Lett, 22 (2009), 64–69. [30] S. R. Tate and H. T. Dinde, Ulam stabilities for nonlinear fractional integro-differential equa- tions with constant coefficient via Pachpatte’s inequality, J. Math. Model, 8(3) (2020), 1–22. [31] S. R. Tate and H. T. Dinde, Existence and uniqueness results for nonlinear implicit fractional differential equations with non local conditions, Palest. J .Math, 9(1) (2020), 212–219. [32] S. Tate, H. T. Dinde, Some Theorems on Cauchy Problem for Nonlinear Fractional Differential Equations with Positive Constant Coefficient, Mediterr. J. Math, 14(2) (2017). [33] J. Wang, H. Xiang, and Z. Liu, Existence of concave positive solutions for boundary-value problem of nonlinear fractional differential equation with p-laplacian operator, Int. J. Math. Math. Sci, 1 (2010), 1–17. [34] X. Xu, D. Jiang, and C. Yuan, Multiple positive solutions to singular positone and semipositone Dirichlet-type boundary-value problems of nonlinear fractional differential equations, Nonlinear Anal, 74 (2011), 5685–5696. [35] Q. Yang and W. Yang, Positive solution for q-fractional four-point boundary value problems with pLaplacian operator, J.Inequal.Appl, 481 (2014), 1–14. [36] C. Yuan, D. Jiang, and X. Xu, Singular positone and semipositone boundary value prob- lems of nonlinear fractional differential equations, Math. Probl. Engineering, 1 (2009), 1–17, https://doi.org/10.1155/2009/535209. [37] Q. Zhang, S. Chen, and J. Lu, Upper and lower solution method for fourth-order four point boundary value problems, J Comput and Appl Math, 196 (2006), 387–393.
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Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem