Results 41 to 50 of about 493 (95)
Quantum Extensions of Widder’s Formula via q‐Deformed Calculus
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.In this study, we rigorously established q‐Widder’s formula of first and second kind by employing the q‐integral within a quantum calculus framework. Our approach introduces a novel formulation of the inverse q‐Laplace transform, enabling simplified computation without relying on conventional complex integration methods.
S. S. Naina Mohammed +6 more
wiley +1 more source
, 2018 We present a new rheological model depending on a real parameter $\nu \in [0,1]$ that reduces to the Maxwell body for $\nu=0$ and to the Becker body for $\nu=1$.
Mainardi, Francesco +2 more
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Saigo Fractional q‐Differentiation Operator Involving Generalized q‐Mittag–Leffler Function
Journal of Mathematics, Volume 2025, Issue 1, 2025.The purpose of this study is to obtain the images of the generalized q‐analogue of Mittag–Leffler functions under the Saigo fractional q‐differentiation operator, where its argument consists of a factor xζxq−μ+ξ−θ. Corresponding assertions in terms of Weyl q‐integral operator, Kober q‐integral operator, and Riemann–Liouville q‐integral operator are ...
Mulugeta Dawud Ali +2 more
wiley +1 more source
On uniqueness of the Laplace transform on time scales [PDF]
, 2011 After introducing the concept of null functions, we shall present a uniqueness result in the sense of the null functions for the Laplace transform on time scales with arbitrary graininess.
Karpuz, Basak
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Time Fractional Cable Equation And Applications in Neurophysiology
, 2017 We propose an extension of the cable equation by introducing a Caputo time fractional derivative. The fundamental solutions of the most common boundary problems are derived analitically via Laplace Transform, and result be written in terms of known ...
Castellani, Gastone +2 more
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Journal of Mathematics, Volume 2025, Issue 1, 2025.Controllability concepts have been essential across various disciplines, including control theory, engineering, and applied mathematics. According to Kalman’s definition, controllability points to the capacity to move a control system’s solution from any initial state to a desired state by a predetermined terminal time.
Maher Jneid, Guotao Wang
wiley +1 more source
Demonstratio MathematicaIn this study, using convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other analytic techniques, the authors verify decreasing property
Yin Hong-Ping, Han Ling-Xiong, Qi Feng
doaj +1 more source
Mellin convolutions of products and ratios
Frontiers in Applied Mathematics and StatisticsUsually, convolution refers to Laplace convolution in the literature, but Mellin convolutions can yield very ueful results. This aspect is illustrated in the coming sections. This study deals with Mellin convolutions of products and ratios.
Arak M. Mathai, Hans J. Haubold
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Convolution Products in L1(R+), Integral Transforms and Fractional Calculus [PDF]
, 2005 Mathematics Subject Classification: 43A20, 26A33 (main), 44A10, 44A15We prove equalities in the Banach algebra L1(R+). We apply them to integral transforms and fractional calculus.* Partially supported by Project BFM2001-1793 of the MCYT-DGI and FEDER ...
Miana, Pedro
core
, 2015 This paper derives new integral representations for products of two parabolic cylinder functions. In particular, expressions are obtained for D_{nu}(x)D_{mu}(y), with x>0 and y>0, that allow for different orders and arguments in the two parabolic ...
Veestraeten, Dirk
core +1 more source