Relatively Uniform Weighted Summability Based on Fractional-Order Difference Operator

Kadak, Uğur; Srivástava, H. M.; Mursaleen, M.

doi:10.1007/s40840-018-0612-2

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Introduction Preliminaries and Definitions1

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2020

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“…Quite recently, the notion of difference sequence spaces based on fractional order was provided by Baliarsingh 5 (see also Baliarsingh and Dutta 6,7 ), and the idea was directly being used to study the fractional derivatives of some functions and their geometrical interpretations. More investigations and applications of related difference sequence spaces are found in previous studies 3,4,8–33 …”

Section: Introduction Preliminaries and Definitionsmentioning

confidence: 93%

On certain dynamic properties of difference sequences and the fractional derivatives

Baliarsingh

2020

Math Methods in App Sciences

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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.

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Section: Introduction Preliminaries and Definitionsmentioning

confidence: 93%

On certain dynamic properties of difference sequences and the fractional derivatives

Baliarsingh

2020

Math Methods in App Sciences

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Relatively equi-statistical convergence via deferred Nörlund mean based on difference operator of fractional-order and related approximation theorems

Jena¹,

Paikray²,

Mohiuddine³

et al. 2020

AIMS Mathematics

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Relatively Uniform Weighted Summability Based on Fractional-Order Difference Operator

Cited by 2 publications

References 37 publications

On certain dynamic properties of difference sequences and the fractional derivatives

On certain dynamic properties of difference sequences and the fractional derivatives

Relatively equi-statistical convergence via deferred Nörlund mean based on difference operator of fractional-order and related approximation theorems

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Relatively Uniform Weighted Summability Based on Fractional-Order Difference Operator

Cited by 2 publications

References 37 publications

On certain dynamic properties of difference sequences and the fractional derivatives

On certain dynamic properties of difference sequences and the fractional derivatives

Relatively equi-statistical convergence via deferred N&#246;rlund mean based on difference operator of fractional-order and related approximation theorems

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Product

Resources

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Relatively equi-statistical convergence via deferred Nörlund mean based on difference operator of fractional-order and related approximation theorems