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Języki publikacji
Abstrakty
In this study, we addressed the nonoscillation of the Sturm-Liouville differential equation with a differential operator, which corresponds to a proportional-derivative controller. The equation is a conformable linear differential equation. A Wintner-type nonoscillation theorem was established to be applied to such equations. Using this theorem, we provided a sharp nonoscillation condition that guarantees that all nontrivial solutions to Euler-type conformable linear equations do not oscillate. The main nonoscillation theorems can be proven by introducing a Riccati inequality, which corresponds to the conformable linear equation of the Sturm-Liouville type.
Czasopismo
Rocznik
Tom
Strony
727--748
Opis fizyczny
Bibliogr. 28 poz., wykr.
Twórcy
autor
- Department of Electrical Systems Engineering, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima 731-5193, Japan
Bibliografia
- [1] T. Abdeljawad, On conformable fractional calculus, J. Comp. Appl. Math. 279 (2015), 57–66.
- [2] M. Abu-Shady, M.K. Kaabar, A generalized definition of the fractional derivative with applications, Math. Probl. Eng. 2021 (2021), 9444803.
- [3] R.P. Agarwal, S.R. Grace, D. O’Regan, Oscillation Theory for Second Order Linear, Half-linear, Superlinear and Sublinear Dynamic Equations, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002.
- [4] K. Ahmed, C. Ahmed, H. Khalid, O. Mohamed, A new conformable fractional derivative and applications, Int. J. Differ. Equ. 2021 (2021), 6245435.
- [5] P. Ahuja, A. Ujlayan, D. Sharma, H. Pratap, Deformable Laplace transform and its application, Nonlinear Eng. 12 (2023), 20220278.
- [6] N. Aliman, R. Ramli, S.M. Haris, M.S. Amiri, M. Van, A robust adaptive-fuzzy-proportional-derivative controller for a rehabilitation lower limb exoskeleton, Eng. Sci. Technol. Int. J. 35 (2022), 101097.
- [7] D.R. Anderson, Second-order self-adjoint differential equations using a proportional-derivative controller, Appl. Nonlinear Anal. 24 (2017), 17–48.
- [8] D.R. Anderson, Even-order self-adjoint boundary value problems for proportional derivatives, Electron. J. Differential Equations 2017 (2017), 1–18.
- [9] D.R. Anderson, S.G. Georgiev, Conformable Dynamic Equations on Time Scales, CRC Press, Boca Raton, FL, 2020.
- [10] D.R. Anderson, D.J. Ulness, Newly defined conformable derivatives, Adv. Dyn. Syst. Appl. 10 (2015), 109–137.
- [11] F.A. Ҫetinkaya, T. Cuchta, Sturm–Liouville and Riccati conformable dynamic equations, Adv. Dyn. Syst. Appl. 15 (2020), 1–13.
- [12] F. Ҫetinkaya, A review of the evolution of the conformable derivatives, Funct. Differ. Equ. 29 (2022), 23–37.
- [13] H. Chhabra, V. Mohan, A. Rani, V. Singh, Robust nonlinear fractional order fuzzy PD plus fuzzy I controller applied to robotic manipulator, Neural Comput. Appl. 32 (2020), 2055–2079.
- [14] O. Došlý, Methods of oscillation theory of half-linear second order differential equations, Czechoslovak Math. J. 50 (2000), 657–671.
- [15] O. Došlý, P. Řehák, Half-linear Differential Equations, North-Holland Mathematics Studies, vol. 202, Amsterdam, 2005.
- [16] F. Gao, C. Chi, Improvement on conformable fractional derivative and its applications in fractional differential equations, J. Funct. Spaces 2020 (2020), 5852414.
- [17] K. Ishibashi, Hille–Nehari type non-oscillation criteria for half-linear dynamic equations with mixed derivatives on a time scale, Electron. J. Differential Equations 2021 (2021), Article no. 78, pp. 15.
- [18] K. Ishibashi, Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations, Opuscula Math. 43 (2023), 67–79.
- [19] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65–70.
- [20] A. Kneser, Untersuchungen über die reellen Nullstellen der Integrale linearer Differentialgleichungen, Math. Ann. 44 (1893), 409–435.
- [21] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, North-Holland Mathematics Studies, Elsevier, Amsterdam, 2006.
- [22] R.A. Moore, The behavior of solutions of a linear differential equation of second order, Pacific J. Math. 5 (1955), 125–145.
- [23] M.D. Ortigueira, J.T. Machado, What is a fractional derivative?, J. Comput. Phys. 293 (2015), 4–13.
- [24] C.A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, Mathematics in Science and Engineering, vol. 48, Academic Press, New York – London, 1968.
- [25] A. Wintner, On the non-existence of conjugate points, Amer. J. Math. 73 (1951), 368–380.
- [26] S.D. Wray, Integral comparison theorems in oscillation theory, J. Lond. Math. Soc. (2) 8 (1974), 595–606.
- [27] F. Wu, J. Sugie, A new application method for nonoscillation criteria of Hille–Wintner type, Monatsh. Math. 183 (2017), 201–218.
- [28] L.G. Zivlaei, A.B. Mingarelli, On the basic theory of some generalized and fractional derivatives, Fractal and Fractional 6 (2022), 672.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-99980706-4fe6-4929-97db-d68693fef422