Abstract
The main objective of this paper is finding new types of discrete transforms with tuning factor t. This is not only analogy to the continuous Laplace transform but gives discrete Laplace-Fibonacci transform (LFt). This type of Laplace-Fibonacci transform is not available in the continuous case. The LFt generates uncountably many outcomes when the parameter t varies on (0,∞). This possibility is not available in the existing Laplace transform. All the formulae and results derived are verified by MATLAB.
References
[1] Bastos.N. R. O, Ferreira.R. A. C, and Torres.D. F. M. Discrete-Time Fractional Variational Problems, Signal Processing, 91(3)(2011),513 - 524.10.1016/j.sigpro.2010.05.001Search in Google Scholar
[2] Britto Antony Xavier.G, Gerly.T.G and Nasira Begum.H, Finite Series of Polynomials and Polynomial Factorials arising from Generalized q-Di_erence operator, Far East Journal of Mathematical Sciences,94(1)(2014), 47 - 63.Search in Google Scholar
[3] Falcon.S and Plaza.A, "On the Fibonacci k−numbers"’, Chaos, Solitons and Fractals, vol.32, no.5 (2007), pp. 1615 - 1624.Search in Google Scholar
[4] Ferreira.R. A. C and Torres.D. F. M, Fractional h-difference equations arising from the calculus of variations, Applicable Analysis and Discrete Mathematics, 5(1) (2011), 110 - 121.10.2298/AADM110131002FSearch in Google Scholar
[5] Jeremy F. Alm and Taylor Herald, A Note on Prime Fibonacci Sequences, Fibonacci Quarterly, 54 (2016), no. 1, 55 - 58.Search in Google Scholar
[6] Jerzy Popenda and Blazej Szmanda, On the Oscillation of Solutions of Certain Dfference Equations, Demonstratio Mathematica, XVII(1), (1984), 153 - 164.10.1515/dema-1984-0114Search in Google Scholar
[7] Koshy.T, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, NY, USA, 2001.10.1002/9781118033067Search in Google Scholar
[8] Koshy.T, Graph-Theoretic Models for the Univariate Fibonacci Family, Fibonacci Quarterly, 53 (2015), no. 2, 135 - 146.Search in Google Scholar
[9] M. Lawrence Glasser and Yajun Zhou, An Integral Representation for the Fibonacci Numbers and Their Generalization, Fibonacci Quarterly, 53 (2015), no. 4, 313 - 318.Search in Google Scholar
[10] Mahadi Ddamulira, Florian Luca and Mihaja Rakotomalala, Fibonacci Numbers Which are Products of Two Pell Numbers, Fibonacci Quarterly, 54 (2016), no. 1, 11 - 18.Search in Google Scholar
[11] Martin Griffths and William Wynn-Thomas, A Property of a Fibonacci Staircase, Fibonacci Quarterly, 53 (2015), no. 1, 61 - 67.Search in Google Scholar
[12] Maria Susai Manuel.M, Britto Antony Xavier.G and Thandapani.E, Theory of Generalized Difference Operator and Its Applications, Far East Journal of Mathematical Sciences, 20(2) (2006), 163 - 171.Search in Google Scholar
[13] Maria Susai Manuel.M, Chandrasekar.V and Britto Antony Xavier.G, Solutions and Applications of Certain Class of α- Difference Equations, International Journal of Applied Mathematics, 24(6) (2011), 943 - 954.Search in Google Scholar
[14] Melham.R.S, On Certain Families of Finite Reciprocal Sums that Involve Generalized Fibonacci Numbers, Fibonacci Quarterly, 53 (2015), no. 4, 323 - 334.Search in Google Scholar
[15] Melham.R.S, More New Algebraic Identities and the Fibonacci Summations Derived From Them, Fibonacci Quarterly, 54 (2016), no. 1, 31 - 43.Search in Google Scholar
[16] Miller.K.S and Ross.B, Fractional Difference Calculus in Univalent Functions, Horwood, Chichester, UK, (1989),139 - 152.Search in Google Scholar
[17] Susai Manuel.M, Britto Antony Xavier.G, Chandrasekar.V and Pugalarasu.R, Theory and application of the Generalized Difference Operator of the nth kind(Part I), Demonstratio Mathematica, 45(1)(2012), 95 - 106.10.1515/dema-2013-0347Search in Google Scholar
[18] Vajda.S, Fibonacci and Lucas Numbers, and the Golden Section, Ellis Horwood, Chichester, UK, 1989.Search in Google Scholar
© 2017
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.