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Neural fractional differential equations
Applied Mathematical ModellingFractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise representation of processes characterised by non-local and memory-dependent behaviours.
C. Coelho +2 more
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SEPARABLE LOCAL FRACTIONAL DIFFERENTIAL EQUATIONS [PDF]
Fractals, 2016 The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators naturally incorporate the fractal sets into the equations.
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The General Fractional Derivative and Related Fractional Differential Equations
Mathematics, 2020 In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine ...
Yuri Luchko, Masahiro Yamamoto
semanticscholar +1 more source
Advances in Difference Equations, 2017 We propose a new method called the fractional reduced differential transform method (FRDTM) to solve nonlinear fractional partial differential equations such as the space-time fractional Burgers equations and the time-fractional Cahn-Allen equation.
Mahmoud S Rawashdeh
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Weak Solutions for Time-Fractional Evolution Equations in Hilbert Spaces
Fractal and Fractional, 2021 Our purpose is to introduce a notion of weak solution for a class of abstract fractional differential equations. We point out that the time fractional derivative occurring in the equations is in the sense of the Caputo derivative.
Paola Loreti, Daniela Sforza
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Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media
, 2011 We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order.
A. A. Kilbas +15 more
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Asymptotic stability of solutions of nonlinear fractional differential equations of order 1 < α < 2
上海师范大学学报. 自然科学版, 2015 This paper is mainly concerned with the asymptotic stability of the solutions of a class of nonlinear fractional differential equations of order 1 < α < 2 in a weighted Banach space.
GE Fudong, KOU Chunhai
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Lie group classifications and exact solutions for time-fractional Burgers equation
, 2010 Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations.
A.B. Malinowska +9 more
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Symmetry Analysis of Initial and Boundary Value Problems for Fractional Differential Equations in Caputo sense [PDF]
, 2019 In this work we study Lie symmetry analysis of initial and boundary value problems for partial differential equations (PDE) with Caputo fractional derivative.
Iskenderoglu, Gulistan, Kaya, Dogan
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Analysis of fractal fractional differential equations
, 2020 Nonlocal differential and integral operators with fractional order and fractal dimension have been recently introduced and appear to be powerful mathematical tools to model complex real world problems that could not be modeled with classical and nonlocal
A. Atangana, Ali Akgül, K. Owolabi
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