Results 21 to 30 of about 12,358 (240)
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 +2 more
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THE 1ST LEVEL GENERAL FRACTIONAL DERIVATIVES AND SOME OF THEIR PROPERTIES [PDF]
Journal of Mathematical Sciences, 2022 In this paper, we first provide a short summary of the main properties of the so-called general fractional derivatives with the Sonin kernels introduced so far.
Yuri Luchko
semanticscholar +1 more source
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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Special Functions of Fractional Calculus in the Form of Convolution Series and Their Applications
Mathematics, 2021 In this paper, we first discuss the convolution series that are generated by Sonine kernels from a class of functions continuous on a real positive semi-axis that have an integrable singularity of power function type at point zero.
Yuri Luchko
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A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String [PDF]
, 2010 We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional versions of the
Almeida, Ricardo +2 more
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Fractional Versions of the Fundamental Theorem of Calculus
Applied Mathematics, 2013 The concept of fractional integral in the Riemann-Liouville, Liouville, Weyl and Riesz sense is presented. Some properties involving the particular Riemann-Liouville integral are mentioned. By means of this concept we present the fractional derivatives, specifically, the Riemann-Liouville, Liouville, Caputo, Weyl and Riesz versions are discussed.
Eliana Contharteze Grigoletto +1 more
openaire +2 more sources
Chemie Ingenieur Technik, EarlyView., 2023 Let us consider an alternative perspective on climate change: The sum of solar radiation and heat generated by human activity result in a net energy input of 1.96 times that of the Sun on the Earth's surface. The expanding global population is expected to exacerbate this issue. Potential solutions are proposed, including replacement and heat recycling.
Martin Bertau, Gerald Steiner
wiley +1 more source
FRACTAL RADIOPHYSICS. Part 3. FRACTIONAL CALCULUS IN ELECTRODYNAMICS [PDF]
Radio Physics and Radio AstronomySubject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed, currently known as fractal radiophysics.
O. V. Lazorenko, L. F. Chernogor
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A generalized fractional order model for COV-2 with vaccination effect using real data
Fractals, 2023 This work is devoted to studying the transmission dynamics of CoV-2 under the effect of vaccination. The aforesaid model is considered under fractional derivative with variable order of nonsingular kernel type known as Atangan-Baleanue-Caputo (ABC ...
Mohammadi Begum Jeelani +5 more
semanticscholar +1 more source
Some fundamental properties on the sampling free nabla Laplace transform
, 2020 Discrete fractional order systems have attracted more and more attention in recent years. Nabla Laplace transform is an important tool to deal with the problem of nabla discrete fractional order systems, but there is still much room for its development ...
Chen, YangQuan +3 more
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