Yıl: 2019 Cilt: 32 Sayı: 4 Sayfa Aralığı: 1238 - 1252 Metin Dili: İngilizce DOI: 10.35378/gujs.493396 İndeks Tarihi: 14-04-2020

Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations

Öz:
This paper examines Hyers-Ulam (HU), Hyers-Ulam-Rassias (HUR) and HyersUlam-Rassias-Gavruta (HURG) stability of the first-order differential equation including Bernoulli’s, Riccati and Abel with given initial condition.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Hyers, D.H.,“On the stability of the linear functional equation”, Proceeding of the National Academy of Sciences of the United States of America, 27: 222-224, (1941).
  • [2] Bourgin, D.G., “Classes of transformations and bordering transformations”, Bulletin of the American Mathematical Society, 57: 223-237, (1951).
  • [3] Aoki, T., “On the stability of the linear transformation in Banach spaces”, Journal of Mathematical Society of the Japan, 2: 64-66, (1950).
  • [4] Rassias, Th.M. “On the stability of the linear mapping in Banach spaces”, Proceeding American Mathematical Society, 72(2): 297-300, (1978).
  • [5] Obloza, M., “Hyers stability of the linear differential equation”, Rocznik Nauk-Dydakt Prace Matematik, 13(1): 259-270, (1993).
  • [6] Obloza, M., “Connections between Hyers and Lyapunov stability of the ordinary differential equations”, Rocznik Nauk-Dydakt Prace Matematik, 14(1): 141-146, (1997).
  • [7] Alsina, C., Ger, R., “On some inequalities and stability results related to the exponential function”, Journal of Mathematical Inequalities, 2(4): 373-380, (1998).
  • [8] Miura, T., “On the Hyers-Ulam stability of a differentiable map”, Scientiae Mathematicae Japonicae, 55: 17-24, (2002).
  • [9] Miura, T., Takahasi, S.E., Choda, H., “On the Hyers-Ulam stability of real continuous function valued differentiable map”, Tokyo Journal of Mathematics, 24: 467-476, (2001).
  • [10] Takahasi, S.E., Miura, T., Miyajima, S., “On the Hyers-Ulam stability of the Banach space-valued differential equation 𝑦′ = 𝜆𝑦”, Bulletin of Korean Mathematical Society, 39: 309-315, (2002).
  • [11] Miura, T., Jung, S.M., Takahasi, S.E., “Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations 𝑦′ = 𝜆𝑦”, Journal of the Korean Mathematical Society, 41: 995-1005, (2004).
  • [12] Jung, S.M., “Hyers-Ulam stability of linear differential equations of first order”, Applied Mathematics Letters, 17(10): 1135-1140, (2004).
  • [13] Jung, S.M., “Hyers-Ulam stability of linear differential equations of first order II”, Applied Mathematics Letters, 19(9): 854-858, (2006).
  • [14] Miura, T., Miyajima, S., Takahasi, S.E., “A characterization of Hyers-Ulam stability of first order linear differential operators”, Journal of Mathematical Analysis Applications, 286: 136-146, (2003).
  • [15] Takahasi, S.E., Takagi, H., Miura, T., Miyajima, S.,“The Hyers-Ulam stability constants of first order linear differential operators”, Journal of Mathematical Analysis Applications, 296: 403-409, (2004).
  • [16] Jung, S.M., “Hyers-Ulam stability of linear differential equations of first order III”, Journal of Mathematical Analysis Applications, 311(1): 139-146, (2005).
  • [17] Wang, G., Zhou, M., Sun, L., “Hyers-Ulam stability of linear differential equations of first order”, Applied Mathematics Letters, 21: 1024-1028, (2008).
  • [18] Jung, S.M., Rassias, T.M., “Generalized Hyers-Ulam stability of Riccati differential equation”, Mathematical Inequalities and Applications, 11(4): 777-782, (2008).
  • [19] Rus, I.A., “Ulam stability of ordinary differential equations”, Studia Universitatis ”Babeş-Bolyai”, Mathematica., 54(4): 125-134, (2009).
  • [20] Rus, I.A., “Ulam stabilities of ordinary differential equations in a Banach space”, Carpathian Journal of Mathematics, 26(1): 103-107, (2010).
  • [21] Jung, S.M., “A fixed point approach to the stability of differential equations 𝑦′ = 𝐹(𝑥,𝑦)”, Bulletin of the Malaysian Mathematical Sciences Society, (2) 33(1): 47-56, (2010).
  • [22] Cãdariu, L., Radu, V.,“On the Stability of the Cauchy Functional Equation: A Fixed Point Approach”, Grazer Mathematische Berichte, 346: 43-52, (2004).
  • [23] Li, X., Wang, J., “Ulam-Hyers-Rassias stability of semilinear differential equations with impulses”, Electronic Journal of Differential Equations, 2013(172): 1-8, (2013).
  • [24] Alqifiary, Q.H., “Note on the stability for linear systems of differential equations”, International Journal of Applied Mathematical Research, 3(1): 15-22, (2014).
  • [25] Qarawani, M.N.,“On Hyers-Ulam-Rassias stability for Bernoulli’s and first order linear and nonlinear differential equations”, British Journal of Mathematics and Computer Science, 4(11): 1615-1628, (2014).
  • [26] Onitsuka, M., Shoji, T.,“Hyers-Ulam stability of first-order homogeneous linear differential equations with a real-valued coefficient”, Applied Mathematics Letters, 63: 102-108, (2017).
  • [27] Jung, S.M., Brzdek, J., “Hyers-Ulam stability of the delay equation 𝑦′(𝑡) = 𝜆𝑦(𝑡 − 𝜏)”,Abstract and Applied Analysis 2010, Article ID 372176, 10 pages (2010).
  • [28] Otrocol, D., Ilea, V., “Ulam stability for a delay differential equation”, Central European Journal of Mathematics, 7: 1296-1303, (2013).
  • [29] Tunç, C., Biçer, E., “Hyers-Ulam-Rassias stability for a first-order functional differential equation”, Journal of Mathematical and Fundamental Sciences, 47(2): 143-153, (2015).
  • [30] Zada, A., Shah, S.O., “Hyers–Ulam stability of first–order non–linear delay differential equations with fractional integrable impulses”, Hacettepe Journal of Mathematics and Statistics, 47(5): 1196–1205, (2018).
  • [31] Zada, A., Ali, W., Park, C., “Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall– Bellman–Bihari’s type”, Applied Mathematics and Computation, 350: 60–65, (2019).
  • [32] András, S., Mészáros, A.R., “Ulam-Hyers stability of dynamic equations on time scales via Picard operators”, Applied Mathematics and Computation, 219: 4853-4864, (2013).
  • [33] Shen, Y., “The Ulam stability of first order linear dynamic equations on time scales”, Results in Mathematics, Online first. (2017), 2017 Springer International Publishing AG DOI 10.1007/s00025017-0725-1.
  • [34] Zada, A., Shah, S.O., Ismail, S., Li, T., “Hyers-Ulam stability in terms of dichotomy of first order linear dynamic systems”, Punjab University Journal of Mathematics, 49(3): 37-47, (2017).
  • [35] Ali, Z., Zada, A., Shah, K., “Existence and stability analysis of three point boundary value problem”, International Journal of Applied Computational Mathematics, 3(1): 651- 664, (2017).
  • [36] Ali, A., Rabiei, F., Shah,K., “On Ulam’s type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions”, Journal of Nonlinear Sciences and Applications, 10: 4760-4775, (2017).
  • [37] Shah, K., Tunç, C., “Existence theory and stability analysis to a system of boundary value problem”, Journal of Taibah University for Science, 11: 1330-1342, (2017).
  • [38] Wang, J., Shah, K., Ali, A., “Existence and Hyers-Ulam stability of fractional Nonlinear Impulsive witched coupled evolution equations”, Mathematical Methods in the Applied Sciences, 41(6): 2392– 2402, (2018).
  • [39] Wang, J., Zada, A., Ali, W., “Ulam’s-type stability of first–order impulsive differential equations with variable delay in quasi–Banach spaces”, International Journal of Nonlinear Sciences and Numerical Simulation, 19(5): 553–560, (2018).
  • [40] Wang, X., Arif, M., Zada, A., “𝛽–Hyers–Ulam–Rassias stability of semilinear nonautonomous impulsive system”, Symmetry, 11(231): 18 pages, (2019).
  • [41] Zada, A., Ali, S., “Stability analysis of multi-point boundary value problem for sequential fractional differential equations with non-instantaneous impulses”, International Journal of Non-linear Sciences and Numerical Simulation, 19(7): 763–774, (2018).
  • [42] Zada, A., Yar, M., Li, T., “Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions”, Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 17: 103–125, (2018).
  • [43] Zada, A., Shaleena, S., Li, T., “Stability analysis of higher order nonlinear differential equations in 𝛽– normed spaces”, Mathematical Methods in the Applied Sciences, 42(4): 1151–1166, (2019).
APA BAŞCI Y, Öğrekçi S, Mısır A (2019). Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. , 1238 - 1252. 10.35378/gujs.493396
Chicago BAŞCI Yasemin,Öğrekçi Süleyman,Mısır Adil Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. (2019): 1238 - 1252. 10.35378/gujs.493396
MLA BAŞCI Yasemin,Öğrekçi Süleyman,Mısır Adil Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. , 2019, ss.1238 - 1252. 10.35378/gujs.493396
AMA BAŞCI Y,Öğrekçi S,Mısır A Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. . 2019; 1238 - 1252. 10.35378/gujs.493396
Vancouver BAŞCI Y,Öğrekçi S,Mısır A Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. . 2019; 1238 - 1252. 10.35378/gujs.493396
IEEE BAŞCI Y,Öğrekçi S,Mısır A "Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations." , ss.1238 - 1252, 2019. 10.35378/gujs.493396
ISNAD BAŞCI, Yasemin vd. "Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations". (2019), 1238-1252. https://doi.org/10.35378/gujs.493396
APA BAŞCI Y, Öğrekçi S, Mısır A (2019). Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science, 32(4), 1238 - 1252. 10.35378/gujs.493396
Chicago BAŞCI Yasemin,Öğrekçi Süleyman,Mısır Adil Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science 32, no.4 (2019): 1238 - 1252. 10.35378/gujs.493396
MLA BAŞCI Yasemin,Öğrekçi Süleyman,Mısır Adil Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science, vol.32, no.4, 2019, ss.1238 - 1252. 10.35378/gujs.493396
AMA BAŞCI Y,Öğrekçi S,Mısır A Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science. 2019; 32(4): 1238 - 1252. 10.35378/gujs.493396
Vancouver BAŞCI Y,Öğrekçi S,Mısır A Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations. Gazi University Journal of Science. 2019; 32(4): 1238 - 1252. 10.35378/gujs.493396
IEEE BAŞCI Y,Öğrekçi S,Mısır A "Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations." Gazi University Journal of Science, 32, ss.1238 - 1252, 2019. 10.35378/gujs.493396
ISNAD BAŞCI, Yasemin vd. "Hyers-Ulam-Rassias Stability for Abel-Riccati Type First-Order Differential Equations". Gazi University Journal of Science 32/4 (2019), 1238-1252. https://doi.org/10.35378/gujs.493396