Variational iteration method for two fractional systems with boundary conditions

Xu, Bo; Zhang, Yufeng; Zhang, Sheng

doi:10.2298/tsci2203653x

Cited by 3 publications

(3 citation statements)

References 37 publications

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“…Integral transform methods have long been recognized as one of the most powerful means for solving partial diferential equations. However, two signifcant developments have recently been added to the literature [1,2]. Teir applications extend to many phenomena in mathematical physics, engineering, and many other scientifc disciplines.…”

Section: Introductionmentioning

confidence: 99%

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Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’

Sedeeg

2023

Complexity

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The goal of this study is to suggest a new general triple integral transform known as Gamar transform. Next, we compare the current transform to a number of existing triple integral transforms such as those by Laplace, Sumudu, Elzaki, Aboodh, and Laplace–Aboodh–Sumudu. We outline its essential properties and prove some important results, including linearity property, existence theorem, triple convolution theorem, and derivatives properties. Moreover, the proposed new transform is applied to solve some partial differential equations (PDEs) such as Laplace, Mboctara, and Wave equations. The capacity of general triple integral transforms to change PDEs into simple algebraic equations is demonstrated.

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Section: Introductionmentioning

confidence: 99%

“…y)e − (φ(s)x+w(r)y) dxdy, (2) where φ(s) and w(r) are the transform functions for x and y, respectively.…”

Section: Introductionmentioning

confidence: 99%

Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’

Sedeeg

2023

Complexity

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“…Fractional calculus has played an irreplaceable role in many fields and attracted more and more attention [1][2][3][4][5][6][7][8][9][10][11][12][13]. In this paper, we mainly have two contributions.…”

Section: Introductionmentioning

confidence: 99%

Application of Jordan canonical form and symplectic matrix in fractional differential models

Shi

Zhang

et al. 2022

THERM SCI

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Under consideration of this paper is the application of Jordan canonical form and symplectic matrix to two conformable fractional differential models. One is the new conformable fractional vector conduction equation which is reduced by using the Jordan canonical form of coefficient matrix and solved exactly, and the other is the new conformable fractional vector dynamical system with Hamilton matrix and symplectic matrix, which is derived by constructing the conformable fractional Euler-Lagrange equation and using fractional variational principle. It is shown that Jordan canonical form and symplectic matrix can be used to deal with some other conformable fractional differential systems in mathematical physics.

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Non-differentiable fractional odd-soliton solutions of local fractional generalized Broer-Kaup system by extending Darboux transformation

Shi

Zhang

2023

THERM SCI

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In this paper, a local fractional generalized Broer-Kaup (gBK) system is first de?rived from the linear matrix problem equipped with local space and time fractional partial derivatives, i.e, fractional Lax pair. Based on the derived fractional Lax pair, the second kind of fractional Darboux transformation (DT) mapping the old potentials of the local fractional gBK system into new ones is then established. Finally, non-differentiable frcational odd-soliton solutions of the local fractional gBK system are obtained by using two basic solutions of the derived fractional Lax pair and the established fractional DT. This paper shows that the DT can be extended to construct non-differentiable fractional soliton solutions of some local fractional non-linear evolution equations in mathematical physics.

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Variational iteration method for two fractional systems with boundary conditions

Cited by 3 publications

References 37 publications

Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’

Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’

Application of Jordan canonical form and symplectic matrix in fractional differential models

Non-differentiable fractional odd-soliton solutions of local fractional generalized Broer-Kaup system by extending Darboux transformation

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