Abstract
In this paper we treat a fractional bosonic, scalar and vectorial, time equation namely Duffin–Kemmer–Petiau Equation. The fractional variational principle was used, the fractional Euler–Lagrange equations were presented. The wave functions were determined and expressed in terms of Mittag–Leffler function.
Similar content being viewed by others
References
Samko S.G., Kilbas A.A., Marichev O.I.: Fractional Integrals and Derivatives Theory and Applications. Gordon and Breach Science Publishers, New York (1993)
Laskin N.: Fractional quantum mechanics. Phys. Rev. E 62, 3135 (2000)
Wang S., Xu M.: Generalized fractional Schrödinger equation with space–time fractional derivatives. J. Math. Phys. 48, 043502 (2007)
Muslih S.I.: Solutions of a particle with fractional δ-potential in a fractional dimensional space. Int. J. Theor. Phys. 49, 2095 (2010)
Rozmej P., Bandrowski B.: On fractional Schrödinger equation. Comput. Methods Sci. Technol. 16, 191 (2010)
Baleanu D., Muslih S.I.: About fractional supersymmetric quantum mechanics. Czechoslov. J. Phys. 55, 1063 (2005)
Ashyralyevab A., Hicdurmazcd B.: On the numerical solution of fractional Schrödinger differential equations with the Dirichlet condition. Int. J. Comput. Math. 89, 1927 (2012)
Bibi A., Kamran A., Hayat U., Mohyud-Din S.T.: New iterative method for time-fractional Schrodinger equations. World J. Mod. Sim. 9, 89 (2013)
Eid R., Muslih S.I., Baleanu D., Rabei E.: Fractional dimentional harmonic oscillator. Rom. J. Phys. 56, 323 (2011)
Laskin N.: Fractional quantum mechanics and Levy path integrals. Phys. Lett. A 268, 298 (2000)
Bhati M.I., Debnath L.: On fractional Schrodinger and Dirac equations. Int. J. Pure Appl. Math. 15, 1 (2004)
Muslih S.I., Agrawal O.P., Baleanu D.: A fractional Schrö dinger equation and its solution. Int. J. Theor. Phys. 49, 1746 (2010)
Muslih S.I., Agrawal O.P., Baleanu D.: A fractional Dirac equation and its solution. J. Phys. A Math. Theor. 43, 055203 (2010)
Muslih, S.I., Agrawal, O.P., Baleanu, D.: Solutions of a fractional dirac equation. In: Proceedings of the ASME (2009) International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE 2009 August 30–September 2, 2009, San Diego, California, USA
Raspini A.: Simple solutions of the fractional Dirac equation of order 2/3. Phys. Scr. 64, 20 (2001)
Tarasov V.E.: Fractional dynamics of relativistic particle. Int. J. Theor. Phys. 49, 293 (2010)
Petiau, G.: Contribution a la theorie des equations d’ondes corpusculaires. Acad. Roy. Belg. Mem. Collect 16 (1936)
Duffin R.Y.: On the characteristic matrices of covariant systems. Phys. Rev. 54, 1114 (1938)
Kummer N.: The particle aspect of meson theory. Proc. R. Soc. A 173, 91 (1939)
Yetkin T., Havare A.: The massless DKP equation and Maxwell equations in Bianchi type III spacetimes. Chin. J. Phys. 41, 5 (2003)
Nuri U.: Duffin–Kemmer–Petiau Equation, Proca Equatio and Maxwells equation in (1+1) D. Concepts Phys. 2, 273 (2005)
Nedjadi Y., Barrett R.C.: Solution of the central field problem for a Duffin–Kemmer–Petiau vector boson. J. Math. Phys. 19, 87 (1994)
Gómez-Aguilara J.F., Yépez-Martínezb H., Escobar-Jiméneza R.F., Astorga-Zaragozaa C.M., Morales-Mendozac L.J., González-Leec M.: Universal character of the fractional space–time electromagnetic waves in dielectric media. J. Electromagn. Waves Appl. 29, 727 (2015)
Tarasov V.E.: Fractional integro-differential equations for electromagnetic waves in dielectric media. Theor. Math. Phys. 158, 355 (2009)
Muslih S.I., Saddallah M., Baleanu D., Rabei E.: Lagrangian formulation of Maxwell’s field in fractional D dimensional space–time. Rom. J. Phys. 55, 659 (2010)
Stanislavsky A.A.: Hamiltonian formalism of fractional systems. Eur. Phys. J. B 49, 93 (2006)
Agrawal O.P.: Formulation of Euler–Lagrange equations for fractional variational problems. J. Math. Anal. and Appl. 272, 368 (2002)
Podlubny, I.: Fractional Differential Equations. Mathematics in Science and Engineering, vol. 198. Academic Press, New York (1999)
Clark B.C. et al.: Pion-nucleus scattering at medium energies with densities from chiral effective field theories. Phys. Lett. B 427, 231 (1998)
Clark B.C. et al.: Relativistic impulse approximation for meson-nucleus scattering in the Kemmer–Duffin–Petiau formalism. Phys. Rev. Lett. 55, 592 (1985)
Guertin R.F., Wilson T.L.: Noncausal propagation in spin-0 theories with external field interactions. Phys. Rev. D 15, 1518 (1977)
Umezawa H.: Quantum Field Theory. North-Holland, Amsterdam (1956)
Gorenflo R., Kilbas A., Mainardi F., Rogosin S.: Mittag–Leffler functions, related topics and applications. Springer, Berlin (2014)
Mainardi F.: Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos Solitons Fractals 7, 1461 (1996)
Mainardi F., Goren R.: On Mittag–Leffler-type functions in fractional evolution processes. J.Comput. Appl.Math. 118, 283 (2000)
Mainardi F.: The fundamental solutions for the fractional diffusion-wave equation. Appl. Math. Lett. 9(6), 23 (1996)
Mainardi F.: Fractional Calculus and Waves in Linear Viscoelasticity. Imperial College Press, London (2010)
Pillai R.N.: On Mittag–Leffler functions and related distributions. Ann. Inst. Stat. Math. 42(1), 157 (1990)
Chetouani L., Merad M., Boudjedaa T., Lecheheb A.: Solution of Duffin–Kemmer–Petiau Equation for the Step Potential. Int. J. Theor. Phys. 43, 4 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bouzid, N., Merad, M. & Baleanu, D. On Fractional Duffin–Kemmer–Petiau Equation. Few-Body Syst 57, 265–273 (2016). https://doi.org/10.1007/s00601-016-1052-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00601-016-1052-x