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<p>Recently, a generalized fractional difference operator in discrete sense has been introduced by Baliarsingh (Alex Eng J 55(2):1811–1816, 2016), and associated difference sequence spaces were defined. Results related to their topological structures and certain well known formulas in fractional calculus have been studied. An application of this operator, some interesting ideas on violating and dynamic behaviors of fractional derivatives have been demonstrated. In fact, the most of resulting dynamic behaviors are due to the lack of convergence of corresponding difference sequences. In this note, we provide a critical analysis on the convergence of the fractional difference sequences and study their corresponding dynamic behaviors.</p>

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On Certain Properties of Fractional Difference Operator

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • P. Baliarsingh,
  • L. Nayak

摘要

Recently, a generalized fractional difference operator in discrete sense has been introduced by Baliarsingh (Alex Eng J 55(2):1811–1816, 2016), and associated difference sequence spaces were defined. Results related to their topological structures and certain well known formulas in fractional calculus have been studied. An application of this operator, some interesting ideas on violating and dynamic behaviors of fractional derivatives have been demonstrated. In fact, the most of resulting dynamic behaviors are due to the lack of convergence of corresponding difference sequences. In this note, we provide a critical analysis on the convergence of the fractional difference sequences and study their corresponding dynamic behaviors.