PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

On nonlinear fractional neutral differential equation with the ψ-Caputo fractional derivative

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article, the solvability of fractional neutral differential equation involving ψ-Caputo fractional operator is considered usinga Krasnoselskii’s fixed point approach. Also, we establish the uniquenessof the solution under certain conditions. Ulam stabilities for the proposedproblem are discussed. Finally, examples are displayed to aid the applicability of the theory results.
Rocznik
Tom
Strony
99--112
Opis fizyczny
Bibliogr. 36 poz.
Twórcy
autor
  • Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt
Bibliografia
  • [1] I. Akbulut, C. Tunç, On the stability of solutions of neutral differential equations of first order, Interational J. of Mathematics and Computer Science 14 (2019) 849-866.
  • [2] A. Ali, B. Samet, K. Shah, R. Khan, Existence and stability of solution of a toppled systems of differential equations non- integer order, Bound. Value Probl. 2017 (16) (2017) 1-13.
  • [3] Z. Ali, A. Zada, K. Shah, Ulam stability results for the solutions of nonlinear implicit fractional order differential equations, Hacet. J. Math. Stat. 48 (4) (2019) 1092-1109.
  • [4] R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci. Numer. Simul. 44 (2017) 460-481.
  • [5] R. Almeida, A.B. Malinowska, M.T. Monterio, Fractional differential equations with a Caputo derivative with respect to a kernel functions and their applications, Math. Method. Appl. Sci. 41 (2018) 336-352.
  • [6] A. Ardjouni, A. Djoudi, Stability in nonlinear neutral differential equations with variable delays using fixed point theory, Electron. J. Qual. Theory Differ. Equ. 43 (2011), 11 pp.
  • [7] G.M. Bahaa, Optimal control problem for variable-order fractional differential systems with time delay involving Atangana-Baleanu derivatives, Chaos, Solitons and Fractals 122 (2019) 129{142.
  • [8] Y. Basci, S. Ogrekçi, A. Misir, On Hyers-Ulam Stability for Fractional Differential Equations Including the New Caputo-Fabrizio Fractional Derivative, Mediterranean Journal of Mathematics (2019) 16:131.
  • [9] H. Boulares, A. Ardjouni, Y. Laskri, Existence and uniqueness of solutions to fractional order nonlinear neutral differential equations, Applied Mathematics E-Notes 18 (2018) 25-33.
  • [10] D.X. Cuong, On the Hyers-Ulam stability of Riemann-Liouville multi-order fractional differential equations, Afr. Mat. (2019) 30:1041.
  • [11] F. Dong, Q. Ma, Single image blind deblurring based on the fractional-order differential, Computers and Mathematics with Applications 78 (6) (2019) 1960-1977.
  • [12] M. Elettreby, A. Al-Raezah, T. Nabil, Fractional-Order Model of Two-Prey One- Predator System, Mathematical Problems in Engineering 2017 (2017), Article ID 6714538, 12 pp.
  • [13] Y. Guo, Xiao-Bao Shu, Y. Li, F. Xu, The existence and Hyers-Ulam stability of solution for an impulsive Riemann-Liouville fractional neutral functional stochastic differential equation with inffnite delay of order 1 < ά < 2, Bound. Value Probl. (2019) 2019:59.
  • [14] E. Hashemizadeh, A. Ebrahimzadeh, An effcient numerical scheme to solve fractional diffusion-wave and fractional Klein-Gordon equations in fluid mechanics, Physica A: Statistical Mechanics and its Applications 503 (2018) 1189-1203.
  • [15] D.H. Hyers, On the stability of the linear functional equations, Proc. Natl. Acad. Sci. U.S.A 27 (4) (1941) 222-224.
  • [16] D.H. Hyers, G. Isac, T.M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Boston, 1998.
  • [17] S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer, 2011.
  • [18] S.-M. Jung, D. Popa, M.Th. Rassias, On the stability of the linear functional equation in a single variable on complete metric groups, Journal of Global Optimization 59 (2014) 165-171.
  • [19] Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer, 2009.
  • [20] H. Khan, T. Abdeljawad, M. Aslam , R. Khan, A. Khan, Existence of positive solution and Hyers-Ulam stability for a nonlinear singular-delay-fractional differential equation, Advances in Difference Equations, December (2019) 2019:104.
  • [21] A. Khan, H. Khan, J.F. Gomez-Aguilar, T. Abdeljawad, Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffer kernel. Chaos, Solitons and Fractals 127 (2019) 422-427.
  • [22] H. Khan, Y. Li, W. Chen, D. Baleanu, A. Khan, Existence theorems and Hyers-Ulam stability for a coupled system of fractional differential equations with p-Laplacian operator, Boundary Value Problems (2017) 2017:157.
  • [23] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
  • [24] T. Nabil, Krasnoselskii N-Tupled Fixed Point Theorem with Applications to Fractional Nonlinear Dynamical System, Advances in Mathematical Physics 2019 (2019), Article ID 6763842, 9 pp.
  • [25] T. Nabil, A.H. Soliman, A Multidimensional Fixed-Point Theorem and Applications to Riemann-Liouville Fractional Differential Equations, Mathematical Problems in Engineering 2019 (2019), Article ID 3280163, 8 pp.
  • [26] A. Niazi, J. Wei, M. Rehman, D. Jun, Ulam-Hyers-Stability for nonlinear fractional neutral differential equations, Hacet. J. Math. Stat. 48 (2019) 157-169.
  • [27] T.M. Rassias, On the stability of linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (2) (1978) 297-300.
  • [28] T.M. Rassias, On the stability of functional equations and a problem of Ulam, Acta. Appl. Math. 62 (2000) 23-130.
  • [29] I.A. Rus, Ulam stabilites of ordinary Differential Equations in a Banach space, Carpathian J. Math. 20 (2010) 103-107.
  • [30] P.K. Sahoo, Pl. Kannappan, Introduction to Functional Equations, Chapman and Hall/CRC, 2017.
  • [31] D.R. Smart, Fixed Point Theorems, Cambridge Univ. Press, Cambridge, 1980.
  • [32] V.E. Tarasov, E.C. Aifantis, On fractional and fractal formulations of gradient linear and nonlinear elasticity, Acta Mechanica 230 (6) (2019) 2043-2070.
  • [33] D.N. Tien, Fractional stochastic differential equations with applications to finance, J. Math. Anal. Appl. 397 (2013) 338-348.
  • [34] S.M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.
  • [35] E. Zeidler, Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems, Springer, 1986.
  • [36] G.Q. Zeng, J. Chen, Y.X. Dai, L.M. Li, C.W. Zheng, M.R. Chen, Design of fractional order PID controller for automatic regulator voltage system based on multi-objective extremal optimization, Neurocomputing 160 (2015) 173-184.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-56d1d0e2-6ed1-4e60-9057-6598fb50d853
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.