Results 31 to 40 of about 184,534 (322)

Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems

Advances in Difference Equations, 2021
In this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods.
Mohamed Abdelhakem, Doha Mahmoud, Dumitru Baleanu, Mamdouh El-kady   +3 more
doaj   +1 more source

Approximate analytical solutions and applications of pantograph-type equations with Caputo derivative and variable orders

Applied Mathematics in Science and Engineering, 2023
This study presents an efficient method that is suitable for differential equations, both with integer-order and fractional derivatives. This study examines the construction of solutions of fractional differential equations that are associated with ...
M.O. Aibinu, E. Momoniat
doaj   +1 more source

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, A. A. Stanislavsky, A. Carpinteri, A. K. Jonscher, A. K. Jonscher, A. K. Jonscher, G. M. Zaslavsky, P. Debye, R. R. Nigmatullin, R. R. Nigmatullin, R. R. Nigmatullin, S. G. Samko, V. E. Tarasov, V. E. Tarasov, V. V. Novikov, Y. Yilmaz   +15 more
core   +1 more source

Neural fractional differential equations

Applied Mathematical Modelling
Fractional 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, M. Fernanda P. Costa, L.L. Ferrás   +2 more
openaire   +3 more sources

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.
openaire   +2 more sources

Applications of Fractional Differentiation Matrices in Solving Caputo Fractional Differential Equations

Fractal and Fractional, 2023
This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as the collocation points and derived the ...
Zhongshu Wu, Xinxia Zhang, Jihan Wang, Xiaoyan Zeng   +3 more
doaj   +1 more source

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, G. Jmnarie, G.C. Wu, G.C. Wu, G.C. Wu, G.W. Bluman, Guo-Cheng Wu, P.J. Olver, R.K. Gazizov, Z.G. Deng   +9 more
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Improved ()-Expansion Method for the Space and Time Fractional Foam Drainage and KdV Equations

Abstract and Applied Analysis, 2013
The fractional complex transformation is used to transform nonlinear partial differential equations to nonlinear ordinary differential equations. The improved ()-expansion method is suggested to solve the space and time fractional foam drainage and KdV ...
Ali Akgül, Adem Kılıçman, Mustafa Inc   +2 more
doaj   +1 more source

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
doaj   +1 more source

Fractional Equations of Curie-von Schweidler and Gauss Laws

, 2008
The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and integrals of ...
Barrett J H, Curie J, Curie J, Debye P, Debye P, Debye P, Erdelyi A, Gorenflo R, Gorenflo R, Jonscher A K, Jonscher A K, Jonscher A K, Kempfle S, Kilbas A A, Podlubny I, Ramakrishnan T V, Samko S G, Tuncer E, Vasily E Tarasov, von Schweidler E   +19 more
core   +3 more sources