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Variational iteration algorithm-I with an auxiliary parameter for wave-like vibration equations

Journal of Low Frequency Noise, Vibration and Active Control, 2019
In this work, the variational iteration algorithm-I with an auxiliary parameter is used for the analytical treatment of the wave equations and wave-like vibration equations.
Hijaz Ahmad, Tufail A. Khan
doaj +1 more source

A New Computational Method Based on Fractional Integration Operational Matrices for Solving Fractional Integro–Differential Equations

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper presents a new numerical method for solving fractional integro–differential equations. After introducing the necessary preliminary definitions, fractional integration operational matrices are constructed based on fractional Lagrange functions, employed here as fractional basis functions.
Mehdi Delkhosh, Patricia J. Y. Wong
wiley +1 more source

Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices [PDF]

, 2010
We apply the method of skew-orthogonal polynomials (SOP) in the complex plane to asymmetric random matrices with real elements, belonging to two different classes. Explicit integral representations valid for arbitrary weight functions are derived for the
Akemann, G +10 more
core +3 more sources

Improved Analytical Technique Based on Laplace Transform and Homotopy Perturbation Method for Solving Fractional Bratu‐Type Equations

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This study presents a modified Laplace transform homotopy perturbation method (MLT‐HPM) for obtaining approximate solutions for fractional‐order Bratu‐type ordinary differential equations involving Caputo fractional derivatives. The proposed modification introduces a specific rule for selecting the initial solution, replacing the conventional random ...
Ibrahim Hailat, Patricia J. Y. Wong
wiley +1 more source

Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform

Abstract and Applied Analysis, 2013
A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved
Jagdev Singh, Devendra Kumar, A. Kılıçman +2 more
doaj +1 more source

Numerical and Analytical Solutions for a Nonlinear System

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper investigates two nonlinear reaction–diffusion systems: (i) a spatially extended competitive species model and (ii) the FitzHugh–Nagumo system, which serves as a canonical model of excitable media. For the first system, we derive exact closed‐form solutions using the exponential function method; these solutions exhibit spatially periodic ...
Badran Jasim Salim, Dalya Mahmood Merie, Deepali +2 more
wiley +1 more source

Solving One-Dimensional Non-Linear Klein-Gordon Equations via Combining Adomian Polynomials and Rohit Transform Method

Iraqi Journal of Physics
In this study, one-dimensional non-linear Klein-Gordon equations are solved by applying the integral transform known as the Rohit transform method. The approximate solutions of one-dimensional non-linear Klein- Gordon equations are obtained by combining
Rohit Gupta, Rahul Gupta
doaj +1 more source

An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform

Abstract and Applied Analysis, 2013
An efficient approach based on homotopy perturbation method by using sumudu transform is proposed to solve nonlinear fractional Harry Dym equation. This method is called homotopy perturbation sumudu transform (HPSTM).
Devendra Kumar, Jagdev Singh, A. Kılıçman +2 more
doaj +1 more source

Solution of Time‐Fractional Coupled Burgers Equations by the Yang Transform Adomian Decomposition Method

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, the Yang transform Adomian decomposition method (YTADM) is employed in the solution of nonlinear time‐fractional coupled Burgers equations. The technique solves the fractional and nonlinear terms successfully via the Adomian decomposition of the Yang transform.
Mustafa Ahmed Ali, Mehmet Merdan, Yeou Jiann Lim +2 more
wiley +1 more source

Memory‐Dependent Chaotic Dynamics and Stabilization of a Nonlinear Fractional‐Order Financial System With Optimal Control

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This study presents an innovative nonlinear fractional‐order financial model that employs Caputo and Caputo–Fabrizio fractional derivatives to represent the dynamic interactions among interest rates, investment demand, price indices, and income/output. The model is formulated as a system of coupled nonlinear differential equations to encapsulate memory‐
Md. Asraful Islam +3 more
wiley +1 more source

mathematics
adomian decomposition method
laplace transform

caputo operator