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New properties of conformable derivative

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Recently, the conformable derivative and its properties have been introduced. In this work we have investigated in more detail some new properties of this derivative and we have proved some useful related theorems. Also, some new definitions have been introduced.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-02-09
zaakceptowano
2015-08-06
online
2015-12-03
Twórcy
  • Institute of Groundwater Studies, University of the Free State, Nelson Mandela Drive,
    9300 Bloemfontein, South Africa
  • Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankara University,
    06530 Ankara, Turkey and Institute of Space Sciences, Magurele, Bucharest, Romania
  • Department of Mathematics, Faculty of Science, King Abdulaziz University P. O. Box 80257, Jeddah 21589,
    Saudi Arabia
Bibliografia
  • [1] R. Khalil , M. Al Horani, A. Yousef and M. Sababheh “A new definition of fractional derivative” Journal of Computational andApplied Mathematics ,(2014) 65–70.
  • [2] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam,The Netherlands, 2006.
  • [3] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY,USA, 1993.
  • [4] S. G. Samko, A. A. Kilbas, and O. I. Maritchev, Integrals and Derivatives of the Fractional Order and Some of Their Applications,in Russian, Nauka i Tekhnika, Minsk, Belarus, 1987.
  • [5] M. Caputo, “Linear models of dissipation whose Q is almost frequency independent, part II,” Geophysical Journal International,vol. 13, no. 5, pp. 529–539, 1967.
  • [6] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam,The Netherlands, 2006.
  • [7] Abdon Atangana and Aydin Secer, “A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some SpecialFunctions,” Abstract and Applied Analysis, vol. 2013, Article ID 279681, 8 pages, 2013. doi:10.1155/2013/279681.
  • [8] I. Podlubny, “Geometric and physical interpretation of fractional integration and fractional differentiation,” Fractional Calculus andApplied Analysis, vol. 5, no. 4, pp. 367–386, 2002.
  • [9] G. Jumarie, “Modified Riemann-Liouville derivative and fractional Taylor series of non-differentiable functions further results,”Computers & Mathematics with Applications, vol. 51, no. 9-10, pp. 1367–1376, 2006.
  • [10] M. Davison and C. Essex, “Fractional differential equations and initial value problems,” The Mathematical Scientist, vol. 23, no. 2,pp. 108–116, 1998.
  • [11] Abdon Atangana and Adem Kilicman, “Analytical Solutions of the Space-Time Fractional Derivative of Advection DispersionEquation,” Mathematical Problems in Engineering, vol. 2013, Article ID 853127, 9 pages, 2013. doi:10.1155/2013/853127.
  • [12] Abdon Atangana and P. D. Vermeulen, “Analytical Solutions of a Space-Time Fractional Derivative of Groundwater FlowEquation,” Abstract and Applied Analysis, vol. 2014, Article ID 381753, 11 pages, 2014. doi:10.1155/2014/381753.
  • [13] Abdon Atangana, “On the Singular Perturbations for Fractional Differential Equation,” The Scientific World Journal, vol. 2014,Article ID 752371, 9 pages, 2014. doi:10.1155/2014/752371
  • [14] Abdon Atangana and Innocent Rusagara, “On the Agaciro Equation via the Scope of Green Function,” Mathematical Problems inEngineering, vol. 2014, Article ID 201796, 8 pages, 2014. doi:10.1155/2014/201796.
  • [15] Y. Luchko and R. Gorenflo, The Initial Value Problem for Some Fractional Differential Equations with the Caputo Derivative,Preprint Series A08-98, Fachbereich Mathematik und Informatik, Freic Universität, Berlin, Germany, 1998.
  • [16] D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional calculus models and numerical methods, Series on Complexity,Nonlinearity and Chaos, World Scientific, Boston, 2012.
  • [17] Thabet Abdeljawad. On the conformable fractional calculus.Journal of computational and Applied Mathematics, 279, pp. 57-66,2015.[WoS]
  • [18] U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput., vol.218, no.3 pp. 860-865, 2011.
  • [19] D. R. Anderson and R. I. Avery, Fractional-order boundary value problem with Sturm-Liouville boundary conditions, ElectronicJournal of Differential Equations, vol.2015 , no. 29, pp.1-10, 2015.
  • [20] U. N. Katugampola, A new fractional derivative with classical properties, arXiv:1410.6535v2.
  • [21] U. N. Katugampola, New approach to generalized fractional derivatives, B. Math. Anal. App., vol.6 no.4 pp. 1-15, 2014.
  • [22] Batarfi, H., Losada, J., Nieto, J.J., Shammakh, W., Three-point boundary value problems for conformable fractional differentialequations. Journal of Function Spaces 2015 (2015), 706383, 6 pages[WoS]
  • [23] Benkhettou, N., Hassani, S., Torres, D.F.M., A conformable fractional calculus on arbitrary time scales,Journal of King SaudUniversity - Science, In Press, doi:10.1016/j.jksus.2015.05.003[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0081
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