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Title: Generalized K-Fractional Conformable Operators with Applications
Authors: Habib, Siddra
Keywords: Physical Sciences
Issue Date: 2020
Publisher: Government College University, Faisalabad
Abstract: Fractional calculus is the generalization of classical calculus related to differential and integral operators of non-integer (fractional) order. It is as aged as classical calculus but acquiring more significance these days because of its vast applications in numerous fields including physics, fluid dynamics, biology, control theory, image processing, computer networking, signal processing and many others. The ambition of this research work is to define the k-fractional conformable (k-FC) integral and derivative operators, which is the generalization of the recently proposed fractional conformable operators. The generalized k-fractional conformable operators unify many existing fractional operators corresponding to different values of the constraints immersed. We also verify the existence of our newly defined k-conformable operators. We discuss important properties of our newly hosted k-fractional conformable operators. The study of inequalities has been enhanced by the applications of fractional operators. The fractional integral inequalities have drawn the attention of many researchers due to their vast applications and importance in many theoretical and applied fields. We generalize some new integral inequalities using our introduced generalized k-fractional conformable integrals (kF CI) for a finite sequence of n positive decreasing functions, where n ∈ N. This work consigns to the generalizations of certain fractional integral inequalities comprising generalized k-fractional conformable integrals. The classical Chebyshev type inequalities, Chebyshev-Gru¨ss type inequalities, an improved version of Gru¨ss type integral inequality, reverse Minkowski inequality, Po´lyaSzego¨ type inequalities and related applications are presented and derived by invoking generalized k-fractional conformable integrals (k-FCI).
Gov't Doc #: 20969
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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