Results 41 to 50 of about 98 (93)
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
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
Renewal Processes of Mittag-Leffler and Wright Type [PDF]
, 2005 2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the ...
Gorenflo, Rudolf +3 more
core
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
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
On Martínez-Kaabar fractal-fractional double Laplace transformation
Ain Shams Engineering JournalAn extended version of the Martinez-Kaabar fractal-fractional (MKF-F) calculus theory is investigated in this work, to the integral transformations and employed in solving some fractal-fractional (F-F) partial integro-differential equations. Specifically,
Francisco Martínez +1 more
doaj +1 more source
Post-Widder inversion for Laplace transforms of hyperfunctions
, 2020 . We prove a Post-Widder inversion formula for the Laplace transform of hyperfunctions with compact support in [0, ∞). We observe that any hyperfunction with support in [0, ∞) has Laplace transforms which are analytic on the right half plane C+, and we ...
Christian Kunstmann
core
Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey [PDF]
, 2007 2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order.
Gorenflo R. +2 more
core
α-Mellin Transform and One of Its Applications [PDF]
, 2012 MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45We consider a generalization of the classical Mellin transformation, called α-Mellin transformation, with an arbitrary (fractional) parameter α > 0. Here we continue the presentation from the paper [5], where we
Nikolova, Yanka
core
Fractional Calculus of P-transforms [PDF]
, 2010 MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99The fractional calculus of the P-transform or pathway transform which is a generalization of many well known integral transforms is studied. The Mellin and Laplace transforms of a P-transform are obtained.
Kumar, Dilip, Kilbas, Anatoly
core