On a fractional difference operator

By Pinakadhar Baliarsingh. 2016

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Abstract In the present article, a set of new difference sequence spaces of fractional order has been introduced and subsequently, an application of these spaces, the notion of the derivatives and the integrals of a function to the case of non-integer order have been generalized. Certain results involving the unusual and non-uniform behavior of the corresponding difference operator have been investigated and also been verified by using some counter examples. We also verify these unusual and non-uniform behaviors by studying the geometry of fractional calculus.

Subfields: Applied Mathematics, Modeling and Simulation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f4e6df77a0aa530253e802a95142d06a92dfb55d