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Abelian Groups of Fractional Operators
Computer Sciences & Mathematics Forum, 2022 Taking into count the large number of fractional operators that have been generated over the years, and considering that their number is unlikely to stop increasing at the time of writing this paper due to the recent boom of fractional calculus ...
Anthony Torres-Hernandez +2 more
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Entropy Interpretation of Hadamard Type Fractional Operators: Fractional Cumulative Entropy [PDF]
Entropy, 2022 Interpretations of Hadamard-type fractional integral and differential operators are proposed. The Hadamard-type fractional integrals of function with respect to another function are interpreted as an generalization of standard entropy, fractional ...
Vasily E. Tarasov
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New Inequalities Using Multiple Erdélyi–Kober Fractional Integral Operators
Fractal and FractionalThe role of fractional integral inequalities is vital in fractional calculus to develop new models and techniques in the most trending sciences. Taking motivation from this fact, we use multiple Erdélyi–Kober (M-E-K) fractional integral operators to ...
Asifa Tassaddiq +4 more
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On the Definitions of Nabla Fractional Operators [PDF]
Abstract and Applied Analysis, 2012 We show that two recent definitions of discrete nabla fractional sum operators are related. Obtaining such a relation between two operators allows one to prove basic properties of the one operator by using the known properties of the other. We illustrate
Thabet Abdeljawad, Ferhan M. Atici
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On Fractional GJMS Operators [PDF]
Communications on Pure and Applied Mathematics, 2015 We describe a new interpretation of the fractional GJMS operators as generalized Dirichlet‐to‐Neumann operators associated to weighted GJMS operators on naturally associated smooth metric measure spaces. This gives a geometric interpretation of the Caffarelli‐Silvestre extension for (−Δ)γ when γ ∊ (0,1), and both a geometric interpretation and a curved
Case, Jeffrey S., Chang, Sun-Yung Alice
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Applications of variable-order fractional operators: a review [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2020 Sansit Patnaik +2 more
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On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function
Mathematics, 2022 The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It is shown that the fractional derivative and integral operators are bounded.
Muhammad Samraiz +5 more
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On the Fractionalization of the Shift Operator on Graphs [PDF]
IEEE Access, 2022 The theory of graph signal processing has been established with the purpose of generalizing tools from classical digital signal processing to the cases where the signal domain can be modeled by an arbitrary graph. In this context, the present paper introduces the notion of fractional shift of signals on graphs, which is related to considering a non ...
Guilherme B. Ribeiro +2 more
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Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions
Journal of Function Spaces, 2022 In this paper, we establish some new Newton’s type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several
Jarunee Soontharanon +5 more
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New Fractional Integral Inequalities via k-Atangana–Baleanu Fractional Integral Operators
Fractal and Fractional, 2023 We propose the definitions of some fractional integral operators called k-Atangana–Baleanu fractional integral operators. These newly proposed operators are generalizations of the well-known Atangana–Baleanu fractional integral operators.
Seth Kermausuor, Eze R. Nwaeze
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