Results 61 to 70 of about 222 (119)
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
A General Class of Multivariable Mittag–Leffler Function and Its Associated Applications
Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.In this paper, a new class of multivariable special functions and their generalizations is introduced and used to solve generalized fractional differential and kinetic equations. By applying the Sumudu transform, we derive solutions for the fractional differential equations and fractional kinetic equations expressed in terms of Prabhakar’s Mittag ...
B. B. Jaimini +5 more
wiley +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
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
Power functions and essentials of fractional calculus on isolated time scales
, 2013 This paper is concerned about a recently suggested axiomatic definition of power functions on a general time scale and its consequences to fractional calculus. Besides a discussion of the existence and uniqueness of such functions, we derive an efficient
Tomáš Kisela
semanticscholar +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
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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
Introducing Bessel functions and their properties
, 2017 A hybrid approach to the introduction of Bessel functions is proposed. Combining the factorization method for resolving second-order homogeneous differential equations into a ladder-operator representation with the Laplace transform method for solving ...
W. Robin
semanticscholar +1 more source
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
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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