Results 1 to 10 of about 6,665 (300)

Operator Kernel Functions in Operational Calculus and Applications in Fractals with Fractional Operators

Fractal and Fractional, 2023
In this study, we delve into the general theory of operator kernel functions (OKFs) in operational calculus (OC). We established the rigorous mapping relation between the kernel function and the corresponding operator through the primary translation ...
Xiaobin Yu, Yajun Yin
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Operational Calculus for the General Fractional Derivatives of Arbitrary Order

Mathematics, 2022
In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin.
Maryam Al-Kandari, Latif A-M. Hanna, Yuri Luchko   +2 more
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Operational Calculus for the 1st-Level General Fractional Derivatives and Its Applications

Mathematics
The 1st-level General Fractional Derivatives (GFDs) combine in one definition the GFDs of the Riemann–Liouville type and the regularized GFDs (or the GFDs of the Caputo type) that have been recently introduced and actively studied in the fractional ...
Maryam Alkandari, Yuri Luchko
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On the solutions of some fractional q-differential equations with the Riemann-Liouville fractional q-derivative [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2021
This paper is devoted to explicit and numerical solutions to linear fractional q -difference equations and the Cauchy type problem associated with the Riemann-Liouville fractional q -derivative in q -calculus.
S. Shaimardan, N.S. Tokmagambetov
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A Provenance Tracking Model for Data Updates [PDF]

Electronic Proceedings in Theoretical Computer Science, 2012
For data-centric systems, provenance tracking is particularly important when the system is open and decentralised, such as the Web of Linked Data. In this paper, a concise but expressive calculus which models data updates is presented.
Gabriel Ciobanu, Ross Horne
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Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense

Mathematics, 2022
In this paper, we first consider the general fractional derivatives of arbitrary order defined in the Riemann–Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of fractional calculus ...
Yuri Luchko
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Construction of Mikusinski operational calculus based on the convolution algebra of distributions. Basic provisions

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012
The main provisions of the operational calculus based on the convolution algebra of distributions D+ and D− that extends this method to the negative values of the argument are given.
Iosif L Kogan
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Construction of Mikusinski operational calculus based on the convolution algebra of distributions. The theorems and the beginning of use

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013
We consider the Mikusinski operational calculus based on the convolution algebra of distributions D′+ and D′−. We state and prove the basic theorems, and give examples of Mikusinski operational calculus using, which demonstrate its additional ...
I. L. Kogan
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A Hypergraph Model for Communication Patterns

Axioms, 2021
The article deals with interaction in concurrent systems. A calculus able to express specific communication patterns is defined, together with its abstract control structures. A hypergraph model for these structures is presented. The hypergraphs are able
Gabriel Ciobanu
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First Class Call Stacks: Exploring Head Reduction [PDF]

Electronic Proceedings in Theoretical Computer Science, 2016
Weak-head normalization is inconsistent with functional extensionality in the call-by-name λ-calculus. We explore this problem from a new angle via the conflict between extensionality and effects. Leveraging ideas from work on the λ-calculus with control,
Philip Johnson-Freyd, Paul Downen, Zena M. Ariola   +2 more
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