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On certain dynamic properties of difference sequences and the fractional derivatives
Author(s) -
Baliarsingh Pinakadhar
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6417
Subject(s) - mathematics , fractional calculus , convergence (economics) , consistency (knowledge bases) , sequence (biology) , context (archaeology) , exponent , algebra over a field , chain rule (probability) , pure mathematics , calculus (dental) , discrete mathematics , law of total probability , medicine , paleontology , bayesian probability , linguistics , philosophy , statistics , posterior probability , dentistry , biology , economics , genetics , economic growth
Recently, the notion of difference operators based on fractional‐order is being extensively used in linear algebra, approximation theory, the theory of fractional calculus (FC), and many others. In this paper, an attempt has been taken for studying the convergence of difference sequence and hence analyzing the consistency and validity of certain related formulas. Investigations on basic results involving convergence, linearity, exponent rule, topological properties, Leibniz, and chain rules for fractional derivatives have been incorporated. In this context, some well‐known results have been demonstrated and verified with the help of some illustrative examples.