Results 61 to 70 of about 476 (175)

Generalized Laplace Transform with Adomian Decomposition Method for Solving Fractional Differential Equations Involving ψ-Caputo Derivative

Mathematics
In this study, we introduced the ψ-Laplace transform Adomian decomposition method, which is a combination of the efficient Adomian decomposition method with the generalization of the classical Laplace transform to treat fractional differential equations ...
Mona Alsulami, Mariam Al-Mazmumy, Maryam Ahmed Alyami, Asrar Saleh Alsulami   +3 more
doaj   +1 more source

Numerical Treatment of the Model for HIV Infection of CD4+T Cells by Using Multistep Laplace Adomian Decomposition Method

Discrete Dynamics in Nature and Society, 2012
A new method for approximate analytic series solution called multistep Laplace Adomian Decomposition Method (MLADM) has been proposed for solving the model for HIV infection of CD4+T cells.
Nurettin Doğan
doaj   +1 more source

Finding the general Solution for some extraordinary Differential Equation [PDF]

مجلة التربية والعلم, 2008
This paper has a dual purpose. One purpose is to introduce a method consists of repeatedly applying Riemann-Liouville operator of appropriate order until the equation , ( ) , (q is integer) is transformed into an ordinary differential equation.A second ...
Shayma Murad
doaj   +1 more source

Existence and Uniqueness of Solutions to Initial Value Problems of High‐Order Fractional Fuzzy Differential Equations

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
High‐order fractional fuzzy differential equations show great potential in modeling complex systems with memory effects and uncertainty. Existing qualitative theories seldom involve both Caputo‐type strongly generalized Hukuhara differentiability and coupled integral operators on infinite intervals. This paper presents a systematic investigation of the
Yanli Xi, Wenbin Bao, Mohammad Rezwan Habib   +2 more
wiley   +1 more source

Perturbation of Highly Dispersive Solitons in Optical Metamaterials with Twin-Core Couplers and Power-Law of Self-Phase Modulation by Laplace–Adomian Decomposition

Algorithms
This paper utilizes the Laplace–Adomian decomposition method to numerically investigate the highly dispersive bright soliton solutions in twin-core optical couplers that employ metamaterials as waveguides.
Oswaldo González-Gaxiola, Jehan Saleh Ahmed, Lina S. Calucag, Anjan Biswas   +3 more
doaj   +1 more source

Double ARA–Generalized Laplace Method for Solving (2 +1)–Dimensional Nonlinear Singular Pseudoparabolic Equations

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, Abdelilah Kamal. H. Sedeeg, Ahmad Qazza, Osama Ala′yed, Muhammad Samraiz   +4 more
wiley   +1 more source

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, Norah Sharif Al-Yazidi, Anwarud Din   +2 more
wiley   +1 more source

Approximate Analytical Solutions of the Time‐Fractional Swift–Hohenberg Equation via Yang Transform Adomian Decomposition Method

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, Mehmet Merdan, Serbay Duran   +2 more
wiley   +1 more source

Solution of Caputo Generalized Bagley–Torvik Equation Using the Tarig Transform

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
A fractional‐order differential equation called the Bagley–Torvik equation describes the behavior of viscoelastic damping. We employed the newly defined Tarig transform in this study to find the analytic solution to the Caputo generalized Bagley–Torvik equation.
Lata Chanchlani, Manisha, D. L. Suthar, S. D. Purohit, Ahmed Saoudi   +4 more
wiley   +1 more source

Accuracy Estimation of the Numerical Solutions for Chaotic Regime of the Pendulum With External and Parametric Excitation

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This study involves the development of a framework for checking the accuracy of built‐in algorithms from Mathcad software. The built‐in algorithms used inside Mathcad software include Runge–Kutta method of the fourth order (RK4), Adams method, backward differential formula, AdamsBDF, Radau, Bulstoer, Stiffr, and Stiffb methods.
M. C. Kekana, M. Y. Shatalov, S. E. Fadugba, N. Jeeva, T. O. Tong, Theodore Simos   +5 more
wiley   +1 more source