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On the classes of fractional order difference sequence spaces and their matrix transformations

Author

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  • Baliarsingh, P.
  • Dutta, S.

Abstract

The main purpose of the present article is to introduce the classes of generalized fractional order difference sequence spaces ℓ∞(Γ,Δα̃,p),c0(Γ,Δα̃,p) and c(Γ,Δα̃,p) by defining the fractional difference operator Δα̃xk=∑i=0∞(-1)iΓ(α̃+1)i!Γ(α̃-i+1)xk+i, where α̃ is a positive proper fraction and k∈N={1,2,3….}. Results concerning the linearity and various topological properties of these spaces are established and also the alpha-, beta-, gamma- and N-duals of these spaces are obtained. The matrix transformations from these classes into Maddox spaces are also characterized. Throughout the article we use the notation Γ(n) as the Gamma function of n, defined by an improper integral Γ(n)=∫0∞e-ttn-1dt, where n∉{0,-1,-2,…} and Γ(n+1)=nΓ(n).

Suggested Citation

  • Baliarsingh, P. & Dutta, S., 2015. "On the classes of fractional order difference sequence spaces and their matrix transformations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 665-674.
  • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:665-674
    DOI: 10.1016/j.amc.2014.10.121
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    Cited by:

    1. Ugur Kadak, 2015. "Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-6, October.

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