New Laplace-type integral transform for solving steady heat-transfer problem

Maitama, Shehu; Zhang, Weidong

doi:10.2298/tsci180110160m

Cited by 10 publications

(6 citation statements)

References 16 publications

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“…Here, we present the definition and properties of the STM which generalize the well-known Laplace transform and the Sumudu integral transform. DEFINITION 1 [10,11] The Shehu transformation of the function q(t) of exponential order is defined over the set of functions,…”

Section: Preliminariesmentioning

confidence: 99%

“…To mention a few, we have the homotopy perturbation method (HPM) [6], the Adomian decomposition method (ADM) [7], the Laplace decomposition method (LDM) [8], the homotopy perturbation transform method (HPTM) [9], and so on. Besides using the Laplace-type integral transform [10,11], some new efficient iterative techniques with the Caputo fractional derivative [12] and Atangana-Baleanu fractional derivative [13] are developed, for example, see [14][15][16][17][18][19][20][21][22][23][24][25]. Those iterative algorithms are successfully applied to many applications in applied physical science.…”

Section: Introductionmentioning

confidence: 99%

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Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

Maitama¹,

Zhang²

2021

J. Appl. Math. Comput. Mech.

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Using the recently proposed homotopy perturbation Shehu transform method (HPSTM), we successfully construct reliable solutions of some important fractional models arising in applied physical sciences. The nonlinear terms are decomposed using He's polynomials, and the fractional derivative is calculated in the Caputo sense. Using the analytical method, we obtained the exact solution of the fractional diffusion equation, fractional wave equation and the nonlinear fractional gas dynamic equation.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

Maitama¹,

Zhang²

2021

J. Appl. Math. Comput. Mech.

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“…In the year 1990, the Sumudu transform was introduced by Gamage K. Watugala to solve differential equations and control engineering problems. The Sumudu transform is an integral transform similar to the Laplace transform; it is equivalent to the Laplace-Carson transforms [27,28] with the substitution p = 1/u. In Sinhala language, the word Sumudu means "smooth."…”

Section: Introductionmentioning

confidence: 99%

Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation

Richard

Zhang

2021

Journal of Applied Mathematics

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The main purpose of this paper is to solve the nonlinear Schrödinger equation using some suitable analytical and numerical methods such as Sumudu transform, Adomian Decomposition Method (ADM), and Padé approximation technique. In many literatures, we can see the Sumudu Adomian decomposition method (SADM) and the Laplace Adomian decomposition method (LADM); the SADM and LADM provide similar results. The SADM and LADM methods have been applied to solve nonlinear PDE, but the solution has small convergence radius for some PDE. We perform the SADM solution by using the function P L / M · called double Padé approximation. We will provide the graphical numerical simulations in 3D surface solutions of each application and the absolute error to illustrate the efficiency of the method. In our methods, the nonlinear terms are computed using Adomian polynomials, and the Padé approximation will be used to control the convergence of the series solutions. The suggested technique is successfully applied to nonlinear Schrödinger equations and proved to be highly accurate compared to the Sumudu Adomian decomposition method.

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“…Various innovators established the underlying framework, as well as their perspectives on expanding calculus, including Liouville, Hadamard, Caputo, Grunwald, Letnikov, Abel, Riez, Caputo-Fabrizio, Atangana-Baleanu (AB), who researched the use of the fractional derivative and fractional differential equations (FDEs). Numerous essential interactions in electromagnetics, acoustics, viscoelasticity, electrochemistry, and material science are well explained by FDEs [8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Novel Numerical Investigations of Fuzzy Cauchy Reaction–Diffusion Models via Generalized Fuzzy Fractional Derivative Operators

et al. 2021

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The present research correlates with a fuzzy hybrid approach merged with a homotopy perturbation transform method known as the fuzzy Shehu homotopy perturbation transform method (SHPTM). With the aid of Caputo and Atangana–Baleanu under generalized Hukuhara differentiability, we illustrate the reliability of this scheme by obtaining fuzzy fractional Cauchy reaction–diffusion equations (CRDEs) with fuzzy initial conditions (ICs). Fractional CRDEs play a vital role in diffusion and instabilities may develop spatial phenomena such as pattern formation. By considering the fuzzy set theory, the proposed method enables the solution of the fuzzy linear CRDEs to be evaluated as a series of expressions in which the components can be efficiently identified and generating a pair of approximate solutions with the uncertainty parameter λ∈[0,1]. To demonstrate the usefulness and capabilities of the suggested methodology, several numerical examples are examined to validate convergence outcomes for the supplied problem. The simulation results reveal that the fuzzy SHPTM is a viable strategy for precisely and accurately analyzing the behavior of a proposed model.

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New Laplace-type integral transform for solving steady heat-transfer problem

Cited by 10 publications

References 16 publications

Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation

Novel Numerical Investigations of Fuzzy Cauchy Reaction–Diffusion Models via Generalized Fuzzy Fractional Derivative Operators

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