Variational iteration transform method for fractional differential equations
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Interdisciplinary Mathematics"
DOI: 10.1080/09720502.2015.1103001
Abstract: Abstract The aim of the work is to extend the application of the modified Variational Iteration Method suggested by Afshan Kanwa and Syed Tauseef Mohyud-Din to obtaining solutions of linear and nonlinear linear time-fractional equations… read more here.
Keywords: iteration; method fractional; iteration transform; variational iteration ... See more keywords
Laplace transform method for the radially deformed Fourier transform
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DOI: 10.1080/10652469.2025.2452911
Abstract: In this paper we consider the kernel of the radially deformed Fourier transform introduced in the context of Clifford analysis in De Bie et al. (The Clifford deformation of the Hermite semigroup. Symmetry Integr Geom.… read more here.
Keywords: transform method; fourier transform; radially deformed; deformed fourier ... See more keywords
Solution to the 1D Stefan problem using the unified transform method
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ac1b79
Abstract: In this paper the one-dimensional two-phase Stefan problem is studied analytically leading to a system of non-linear Volterra-integral-equations describing the heat distribution in each phase. For this the unified transform method has been employed which… read more here.
Keywords: transform method; unified transform; stefan; stefan problem ... See more keywords
The unified transform method: beyond circular or convex domains
Sign Up to like & getrecommendations! Published in 2024 at "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"
DOI: 10.1098/rspa.2025.0313
Abstract: A new transform-based approach is presented that can be used to solve mixed boundary value problems for Laplace’s equation in non-convex and other planar domains, specifically the so-called Lipschitz domains. This work complements Crowdy (2015,… read more here.
Keywords: transform method; convex; unified transform; transform ... See more keywords
Analytical Bending Solutions of Orthotropic Rectangular Thin Plates with Two Adjacent Edges Free and the Others Clamped or Simply Supported Using Finite Integral Transform Method
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DOI: 10.1155/2020/8848879
Abstract: For the first time, the finite integral transform method is introduced to explore the accurate bending analysis of orthotropic rectangular thin plates with two adjacent edges free and the others clamped or simply supported. Previous… read more here.
Keywords: integral transform; method; simply supported; finite integral ... See more keywords
A General Scheme for Solving Systems of Linear First-Order Differential Equations Based on the Differential Transform Method
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DOI: 10.1155/2021/8839201
Abstract: In this study, we develop the differential transform method in a new scheme to solve systems of first-order differential equations. The differential transform method is a procedure to obtain the coefficients of the Taylor series… read more here.
Keywords: transform method; differential transform; first order;
Exact differential transform method and semi-analytic Chebyshev collocation method for ordinary differential equations
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DOI: 10.1186/s13661-025-02019-5
Abstract: This article introduces two algorithms designed for solving differential equations: the differential transform method and the second-kind Chebyshev collocation method. It provides a detailed explanation of the structure and key properties of each method. The… read more here.
Keywords: transform method; differential transform; method; collocation method ... See more keywords
Solving time-fractional chemical engineering equations by generalized differential transform method
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DOI: 10.2298/tsci20s1157h
Abstract: In this paper fractional differential transform method is implemented for modelling and solving system of the time fractional chemical engineering equations. In this method the solution of the chemical reaction, reactor, and concentration equations are… read more here.
Keywords: time fractional; chemical engineering; chemical; fractional chemical ... See more keywords
Analytical Solution of Generalized Bratu-Type Fractional Differential Equations Using the Homotopy Perturbation Transform Method
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DOI: 10.3390/axioms13020133
Abstract: In this study, we present the generalized form of the higher-order nonlinear fractional Bratu-type equation. In this generalization, we deal with a generalized fractional derivative, which is quite useful from an application point of view.… read more here.
Keywords: bratu type; transform method; differential equations; method ... See more keywords
Exploring a Novel Multi-Stage Differential Transform Method Coupled with Adomian Polynomials for Solving Implicit Nonlinear ODEs with Analytical Solutions
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DOI: 10.3390/math13030358
Abstract: In engineering, physics, and other fields, implicit ordinary differential equations are essential to simulate complex systems. However, because of their intrinsic nonlinearity and difficulty separating higher-order derivatives, implicit ordinary differential equations pose substantial challenges. When… read more here.
Keywords: transform method; differential transform; method; stage differential ... See more keywords
Application of Aboodh Homotopy Perturbation Transform Method for Fractional-Order Convection-Reaction-Diffusion Equation within Caputo and Atangana-Baleanu Operators
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DOI: 10.3390/sym15020453
Abstract: This article is an analysis of fractional nonlinear convection–reaction–diffusion equations involving the fractional Atangana–Baleanu and Caputo derivatives. An efficient Aboodh homotopy perturbation transform method, which combines the homotopy perturbation method with the Aboodh transformation, is… read more here.
Keywords: transform method; aboodh homotopy; perturbation; perturbation transform ... See more keywords