Results 41 to 50 of about 26,870 (247)
Alexandria Engineering JournalIn this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the ψ-Caputo–Katugampola fractional derivative (ψ-CKFD).
Lakhlifa Sadek +2 more
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Caputo-type modification of the Hadamard fractional derivatives [PDF]
Advances in Difference Equations, 2012 Abstract Generalization of fractional differential operators was subjected to an intense debate in the last few years in order to contribute to a deep understanding of the behavior of complex systems with memory effect. In this article, a Caputo-type modification of Hadamard fractional derivatives is introduced. The properties of the modified
Fahd Jarad +2 more
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Towards Fractional Gradient Elasticity
, 2013 An extension of gradient elasticity through the inclusion of spatial derivatives of fractional order to describe power-law type of non-locality is discussed. Two phenomenological possibilities are explored.
Aifantis, Elias C., Tarasov, Vasily E.
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Numerical approximations for a fully fractional Allen-Cahn equation
, 2020 A finite element scheme for an entirely fractional Allen-Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, the Caputo fractional in-time derivative and the fractional Laplacian replace the standard ...
Acosta, Gabriel, Bersetche, Francisco
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A Nonlinear Implicit Fractional Equation with Caputo Derivative [PDF]
Journal of Mathematics, 2021 In this paper, we study a nonlinear implicit differential equation with initial conditions. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of Banach principle.
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Prabhakar-like fractional viscoelasticity
, 2017 The aim of this paper is to present a linear viscoelastic model based on Prabhakar fractional operators. In particular, we propose a modification of the classical fractional Maxwell model, in which we replace the Caputo derivative with the Prabhakar one.
Colombaro, Ivano, Giusti, Andrea
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Electrical circuits RC and RL involving fractional operators with bi-order
Advances in Mechanical Engineering, 2017 This article describes electrical series circuits RC and RL using the concept of derivative with two fractional orders α and β in Liouville–Caputo sense. The fractional equations consider derivatives in the range of α , β ∈ ( 0 ; 1 ] .
JF Gómez-Aguilar +4 more
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Journal of Function Spaces, 2020 In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and
Mehnaz Shakeel +5 more
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A PRIORI ESTIMATION OF A GENERALIZED NONLOCAL BOUNDARY VALUE PROBLEM FOR A THRID ORDER EQUATION WITH A FRACTIONAL TIME CAPUTO DERIVATIVE [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2019 A boundary value problem for a third-order parabolic equation with a fractional Caputo derivative is considered. A priori estimation of the solution of a generalized nonlocal boundary value problem for an equation with multiple characteristics with a ...
A. M. Shkhagapsoev
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New applications of the new general integral transform method with different fractional derivatives
Alexandria Engineering Journal, 2023 Integral transforms are a versatile mathematical technique that can be applied in a wide range of science and engineering fields. We consider the general integral transform with the Caputo derivative and Constant Proportional Caputo derivative in this ...
Ali Akgül +4 more
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