m(α)-Series of The Generalized α-Difference Equation to Polynomial Factorial

G.Britto Antony Xavier; H.Nasira Begum

doi:https://doi.org/10.14445/22315373/IJMTT-V11P515

International Journal of Mathematics Trends and Technology

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Volume 11 | Number 2 | Year 2014 | Article Id. IJMTT-V11P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V11P515

m(α)-Series of The Generalized α-Difference Equation to Polynomial Factorial

G.Britto Antony Xavier, H.Nasira Begum

Abstract

In this paper, the authors extend the theory and m-series of the generalized difference equation to m(α)-series of its α-difference equation. We also investigate the complete and summation solutions of certain type of α-difference equation to polynomial factorial with geometric function in the field of finite difference methods.

Keywords

Generalized α-difference equation, summation solution, complete solution, generalized polynomial factorial.

References

[1] Jerzy Popenda and Blazej Szmanda, On the Oscillation of Solutions of Certain Difference Equations, Demonstratio Mathematica, XVII(1), (1984), 153 - 164.
[2] M.Maria Susai Manuel, G.Britto Antony Xavier and E.Thandapani, Theory of Generalized Difference Operator and Its Applications, Far East Journal of Mathematical Sciences, 20(2) (2006), 163 - 171.
[3] R. A. C. Ferreira and D. F. M. Torres, Fractional h-difference equations arising from the calculus of variations, Applicable Analysis and Discrete Mathematics, 5(1) (2011), 110-121.
[4] M.Maria Susai Manuel, G.Britto Antony Xavier, D.S.Dilip and G.Dominic Babu. Oscillation, nonoscillation and growth of solutions of generalized second order nonlinear difference equations. Global J. Math. Sci. Theory and practical,4(1):121:132, 2012.
[5] M. M. Susai Manuel, G.B. A. Xavier, V. Chandrasekar and R. Pugalarasu, Theory and application of the Generalized Difference Operator of the kind(Part I), Demonstratio Mathematica,vol.45,no.1,pp.95-106,2012.
[6] M.Maria Susai Manuel, V.Chandrasekar and G.Britto Antony Xavier, Solutions and Applications of Certain Class of -Difference Equations, International Journal of Applied Mathematics, 24(6) (2011), 943-954.
[7] M.Maria Susai Manuel, V.Chandrasekar and G.Britto Antony Xavier, Theory of Generalized -Difference Operator and its Applications in Number Theory, Advances in Differential Equations and Control Processes, 9(2) (2012), 141-155.
[8] K.S.Miller and B.Ross, Fractional Difference Calculus in Univalent Functions, Fractional Calculus and Their Applications(Koriyama, 1988),pp . 139-152, Horwood, Chichester, UK, 1989.
[9] N. R. O. Bastos, R. A. C. Ferreira, and D. F. M. Torres, Discrete-Time Fractional Variational Problems, Signal Processing, vol.91,no. 3,pp. 513-524, 2011.
[10] M.Maria Susai Manuel, V.Chandrasekar and G.Britto Antony Xavier, Generalized Bernoulli Polynomials through Weighted Pochhammer Symbols Vol. 4, No. 1, 2013, 23-29.
[11] G. Britto Antony Xavier, S. U. Vasanthakumar, and B. Govindan, Discrete Beta-Factorial Function and Its Series in Terms of Closed form solution of Generalized Difference Equation International journal of Mathematical Archive-4(10), Oct.-2013
[12] G. Britto Antony Xavier, S. Sathya and S. U. Vasanthakumar, m-Series Of The Generalized Difference Equation To Circular Functions International journal of Mathematical Archive-4(7), 2013, 200-209.

Citation :

G.Britto Antony Xavier, H.Nasira Begum, "m(α)-Series of The Generalized α-Difference Equation to Polynomial Factorial," International Journal of Mathematics Trends and Technology (IJMTT), vol. 11, no. 2, pp. 102-111, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V11P515