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Duality of Shehu transform with other well known transforms and application to fractional order differential equations. [PDF]
PLoS ONEIntegral transforms are used in many research articles in the literature, due to their interesting applications in the solutions of problems of applied science and engineering.
Nabil Mlaiki +4 more
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Timoshenko beam and plate non-stationary vibrations [PDF]
INCAS Bulletin, 2021 The problems of Timoshenko beams and plates lateral vibrations under the influence of unsteady loads are considered. Both beam and plate is supposed to be unlimited. In case of the plate the problem has been simply studied.
Grigory V. FEDOTENKOV +4 more
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On the Fractional Derivative Duality in Some Transforms
Mathematics, 2023 Duality is one of the most interesting properties of the Laplace and Fourier transforms associated with the integer-order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier
Manuel Duarte Ortigueira +1 more
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Fourier/Laplace Transforms and Ruin Probabilities [PDF]
ASTIN Bulletin, 2002 AbstractIn this paper we use Fourier/Laplace transforms to evaluate numerically relevant probabilities in ruin theory as an application to insurance. The transform of a function is split in two: the real and the imaginary parts. We use an inversion formula based on the real part only, to get the original function.By using an appropriate algorithm to ...
Lima, Fátima D. E. +2 more
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The Fourier–Laplace Transformation and Material Law Operators [PDF]
, 2021 AbstractIn this chapter we introduce the Fourier–Laplace transformation and use it to define operator-valued functions of ∂t,ν; the so-called material law operators. These operators will play a crucial role when we deal with partial differential equations.
Christian Seifert +2 more
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Alexandria Engineering Journal, 2023 The extended thermoelastic theory with fractional derivative is described in this article to estimate temperature variation, displacement components, and stress components in two-dimensional orthotropic materials.
Aatef Hobiny, Ibrahim A. Abbas
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New iterative technique for computing Fourier transforms. [PDF]
مجلة جامعة الانبار للعلوم الصرفة, 2023 The Fourier transformations have stimulated many amounts of articles in recent years. they arise in the fields of engineering, control systems, and technology like analyzing signals in electronic circuits, radio circuits, cell phones, image processing ...
Ahmad Issa, Murat Düz
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The Generalized Fourier Transform: A Unified Framework for the Fourier, Laplace, Mellin and Z Transforms [PDF]
IEEE Transactions on Signal Processing, 2021 <div>This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as proposed in this work, contributes significantly to the scholarly literature.
Pushpendra Singh +2 more
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ABOUT THE EQUALITY OF THE TRANSFORM OF LAPLACE TO THE TRANSFORM OF FOURIER
Проблемы анализа, 2016 We proved that the transform of Laplace does not have complex part on the complex axis for the wide class of functions in different situations. The main theorem is proved presenting a function as sum of two Laplace transforms.
Pavlov Andrey V.
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Fractional Equations for the Scaling Limits of Lévy Walks with Position-Dependent Jump Distributions
Mathematics, 2023 Lévy walks represent important modeling tools for a variety of real-life processes. Their natural scaling limits are known to be described by the so-called material fractional derivatives.
Vassili N. Kolokoltsov
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