Optimal homotopy asymptotic method for solving several models of first order fuzzy fractional IVPs

Hashim, Dulfikar Jawad; Jameel, A. F.; Ying, Teh Yuan; Alomari, A. K.; Anakira, N. R.

doi:10.1016/j.aej.2021.09.060

Cited by 13 publications

(4 citation statements)

References 23 publications

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“…Nowadays, because of various applications of the theory of fuzzy differential equations, many researchers are working on fuzzy partial differential equations. Several researchers emphasized studying the precise/numerical solutions of fuzzy differential equations [5][6][7].…”

Section: Introduction 1research Backgroundmentioning

confidence: 99%

On Fuzzy Conformable Double Laplace Transform with Applications to燩artial Differential Equations

Abdeljawad¹,

Younus²,

Alqudah³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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The Laplace transformation is a very important integral transform, and it is extensively used in solving ordinary differential equations, partial differential equations, and several types of integro-differential equations. Our purpose in this study is to introduce the notion of fuzzy double Laplace transform, fuzzy conformable double Laplace transform (FCDLT). We discuss some basic properties of FCDLT. We obtain the solutions of fuzzy partial differential equations (both one-dimensional and two-dimensional cases) through the double Laplace approach. We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations.

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Section: Introduction 1research Backgroundmentioning

confidence: 99%

On Fuzzy Conformable Double Laplace Transform with Applications to燩artial Differential Equations

Abdeljawad¹,

Younus²,

Alqudah³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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“…Retrieving the analytical solutions for FDEs is sometimes difficult to achieve due to the computational complexities of fractional operators. In this respect, numerous methods have been constructed and motivated to investigate the approximate solution for FDEs, among which are the Sinc-collocation method [27], the predictor-corrector compact difference scheme [28], the variational iteration method [29], the homotopy analysis technique [30], the homotopy asymptotic method [31], the homotopy perturbation scheme [32], the differential transform method [33], the linearly compact scheme [34], the Adomian decomposition method [35] etc.…”

Section: Introductionmentioning

confidence: 99%

Computational Study for Fiber Bragg Gratings with Dispersive Reflectivity Using Fractional Derivative

Tariq¹,

Akram

Sadaf

et al. 2023

Fractal Fract

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In this paper, the new representations of optical wave solutions to fiber Bragg gratings with cubic–quartic dispersive reflectivity having the Kerr law of nonlinear refractive index structure are retrieved with high accuracy. The residual power series technique is used to derive power series solutions to this model. The fractional derivative is taken in Caputo’s sense. The residual power series technique (RPST) provides the approximate solutions in truncated series form for specified initial conditions. By using three test applications, the efficiency and validity of the employed technique are demonstrated. By considering the suitable values of parameters, the power series solutions are illustrated by sketching 2D, 3D, and contour profiles. The analysis of the obtained results reveals that the RPST is a significant addition to exploring the dynamics of sustainable and smooth optical wave propagation across long distances through optical fibers.

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“…Recent works including the OHAM-2 are given by many researchers. Hashimet al 17 considered OHAM-2 for resolving numerous simulations of first-order fuzzy fractional IVPs. Olumide et al 18 studied the efficient result of the fractional-order SIR epidemic exemplary of childhood diseases with OHAM-2.…”

Section: Introductionmentioning

confidence: 99%

New optimum solutions of nonlinear fractional acoustic wave equations via optimal homotopy asymptotic method-2 (OHAM-2)

Zada

Nawaz

Jamshed

et al. 2022

Sci Rep

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The second iteration of the optimal homotopy asymptotic technique (OHAM-2) has been protracted to fractional order partial differential equations in this work for the first time (FPDEs). Without any transformation, the suggested approach can be used to solve fractional-order nonlinear Zakharov–Kuznetsov equations. The Caputo notion of the fractional-order derivative, whose values fall within the closed interval [0, 1], has been taken into consideration. The method's appeal is that it provides an approximate solution after just one iteration. The suggested method's numerical findings have been contrasted with those of the variational iteration method, residual power series method, and perturbation iteration method. Through tables and graphs, the proposed method's effectiveness and dependability are demonstrated.

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Optimal homotopy asymptotic method for solving several models of first order fuzzy fractional IVPs

Cited by 13 publications

References 23 publications

On Fuzzy Conformable Double Laplace Transform with Applications to燩artial Differential Equations

On Fuzzy Conformable Double Laplace Transform with Applications to燩artial Differential Equations

Computational Study for Fiber Bragg Gratings with Dispersive Reflectivity Using Fractional Derivative

New optimum solutions of nonlinear fractional acoustic wave equations via optimal homotopy asymptotic method-2 (OHAM-2)

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