Results 1 to 10 of about 29,190 (163)

Exact solutions for nonlinear fractional differential equations using G′G2-expansion method

Alexandria Engineering Journal, 2018
A relatively new technique which is named as G′G2-expansion method is applied to attain exact solution of nonlinear fractional differential equations (NLFDEs).
Syed Tauseef Mohyud-Din, Sadaf Bibi
doaj   +3 more sources

The G′G-expansion method using modified Riemann–Liouville derivative for some space-time fractional differential equations

Ain Shams Engineering Journal, 2014
In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear ...
Ahmet Bekir, Özkan Güner
doaj   +3 more sources

High-order expansion of neural ordinary differential equation flows. [PDF]

Sci Adv
Artificial neural networks, widely recognized for their role in machine learning, are also transforming the study of ordinary differential equations (ODEs), bridging data-driven modeling with classical dynamical systems as well as enabling the development of infinitely deep neural models. However, their practical applicability remains, in this context,
Izzo D, Origer S, Acciarini G, Biscani F.   +3 more
europepmc   +5 more sources

A comparative analysis of generalized and extended (G′G)-Expansion methods for travelling wave solutions of fractional Maccari's system with complex structure

Alexandria Engineering Journal, 2023
Fractional partial differential equations emerge as a prominent research area in recent times owing to their ability to depict intricate physical phenomena. Discovering travelling wave solutions for fractional partial differential equations is an arduous
Rashid Ali, Elsayed Tag-eldin
doaj   +1 more source

Fractional Differential Equations and Expansions in Fractional Powers

Symmetry, 2023
We use power series with rational exponents to find exact solutions to initial value problems for fractional differential equations. Certain problems that have been previously studied in the literature can be solved in a closed form, and approximate solutions are derived by constructing recursions for the relevant expansion coefficients.
Diego Caratelli, Pierpaolo Natalini, Paolo Emilio Ricci   +2 more
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Solutions of Nonlinear Integro-Partial Differential Equations by the Method of G′/G,1/G

Advances in Mathematical Physics, 2022
In this article, a special expansion method is implemented in solving nonlinear integro-partial differential equations of 2+1-dimensional using a special expansion method of G′/G,1/G.
Daba Meshesha Gusu, Chala Bulo
doaj   +1 more source

Chebyshev expansions for solutions of linear differential equations [PDF]

Proceedings of the 2009 international symposium on Symbolic and algebraic computation, 2009
A Chebyshev expansion is a series in the basis of Chebyshev polynomials of the first kind. When such a series solves a linear differential equation, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators.
Benoit, Alexandre, Salvy, Bruno
openaire   +3 more sources

An Approximate Optimization Method for Solving Stiff Ordinary Differential Equations With Combinational Mutation Strategy of Differential Evolution Algorithm

Mendel, 2022
This paper examines the implementation of simple combination mutation of differential evolution algorithm for solving stiff ordinary differential equations.
Werry Febrianti, Kuntjoro Adji Sidarto, Novriana Sumarti   +2 more
doaj   +1 more source

Expansivity of Nonsmooth Functional Differential Equations

Journal of Mathematical Analysis and Applications, 1997
The paper deals with expansivity of a nonsmooth dynamical system, in which all trajectories that remain within a certain threshold of each other must be identical. Explicit knowledge of the rates of separation is useful for numerical calculations and shadowing arguments.
Al-Nayef, A.A, Kloeden, P.E, Pokrovskii, A.V   +2 more
openaire   +2 more sources

Boundary value problems solving method with the implicit use of the Taylor expansions

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012
Grid method for boundary value problems solving for partial differential equations based on high order Taylor expansions is suggested. Comparison of the proposed method with classical grid method is implemented.
A. A. Usov
doaj   +3 more sources