Results 61 to 70 of about 541 (198)
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
A hybrid analytical algorithm for thin film flow problem occurring in non-Newtonian fluid mechanics
Ain Shams Engineering Journal, 2021 In this work, we investigate thin film flow of a third grade fluid down a inclined plane. The solution of a nonlinear boundary value problem (BVP) is derived by using an effective well organized computational scheme namely homotopy perturbation Elzaki ...
Sushila +3 more
doaj +1 more source
Smooth polynomial expansions of piecewise-differentiable functions
, 1989 This paper proposes an extension of the expansions of analytic functions in the An polynomials defined by Adomian [1] to consider piecewise-differentiable ...
Adomian, G., Rach, R.
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Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.This study presents a novel triple integral transformation, called the double ARA–generalized Laplace transform (DAGLT), and applies it to solve (2 + 1)–dimensional singular pseudoparabolic equations in both linear and nonlinear forms. The work begins by outlining the fundamental definitions, theorems, and characteristics of the single ARA and ...
Rania Saadeh +4 more
wiley +1 more source
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
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On the Coupling of Auxiliary Parameter, Adomian's Polynomials and Correction Functional [PDF]
Mathematical and Computational Applications, 2011 In this paper, we apply He’s variational iteration method (VIM) coupled with an auxiliary parameter and Adomian’s polynomials which proves very effective to control the convergence region of approximate solution. The proposed algorithm is tested on generalized Hirota–Satsuma coupled KdV equation and numerical results explicitly reveal the complete ...
M. Hosseini, Syed Mohyud-Din, H. Ghaneai
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A Reliable Decomposition Method for Fractional‐Order Fokker–Planck Equation
Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.This study analytically investigates the fractional Fokker–Planck equations (F‐FPEs) by employing the Sumudu decomposition method (SDM). This method combines the strengths of the Sumudu transform and the Adomian decomposition method (ADM) to effectively handle the nonlocality and memory characteristics inherent in governing fractional differential ...
Mona Alsulami +2 more
wiley +1 more source
Nonlinear Integro-differential Equations by Differential Transform Method with Adomian Polynomials [PDF]
, 2013 : A modification of differential transformation method is applied to nonlinear integro-differential equations. In this technique, the nonlinear term is replaced by its Adomian polynomials for the index k, and hence the dependent variable components are ...
S. H. Behiry
core
Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.This study examines approximate analytical solutions of the time‐fractional Swift–Hohenberg equation involving the Caputo–Fabrizio fractional derivative. The main objective of this study is to investigate efficient analytical approximation techniques using the Yang transform Adomian decomposition method (YTADM).
Mustafa Ahmed Ali +2 more
wiley +1 more source
A new scheme for the solution of the nonlinear Caputo–Hadamard fractional differential equations
Alexandria Engineering JournalThis paper introduces a numerical approach by generalizing Legendre wavelets for solving nonlinear Caputo–Hadamard fractional differential equations. The methodology involves the extension of classical Legendre wavelets, namely the generalized Legendre ...
Umer Saeed, Mujeeb ur Rehman
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