Application of Laplace residual power series method for approximate solutions of fractional IVP’s

Alaroud, Mohammad

doi:10.1016/j.aej.2021.06.065

Cited by 34 publications

(17 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should be mentioned that there is an exciting recent work on the conformable Euler method for finite difference discretization of FIVPs [ 39 , 40 ] showing that the fractional Taylor expansions in terms of the conformable fractional derivative presented in [ 36 ] is valid for

. An alternative definition of the conformable fractional derivative introduced in [ 40 ] based on the exact spectral derivative discretization finite difference method showing that the conformable fractional derivative [ 36 ] is a fractional change of a variable rather that a fractional operator.…”

Section: Preliminariesmentioning

confidence: 99%

Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense

Bataineh

Alaroud

Al‐Omari

et al. 2021

Entropy

Self Cite

View full text Add to dashboard Cite

Fuzzy differential equations provide a crucial tool for modeling numerous phenomena and uncertainties that potentially arise in various applications across physics, applied sciences and engineering. Reliable and effective analytical methods are necessary to obtain the required solutions, as it is very difficult to obtain accurate solutions for certain fuzzy differential equations. In this paper, certain fuzzy approximate solutions are constructed and analyzed by means of a residual power series (RPS) technique involving some class of fuzzy fractional differential equations. The considered methodology for finding the fuzzy solutions relies on converting the target equations into two fractional crisp systems in terms of ρ-cut representations. The residual power series therefore gives solutions for the converted systems by combining fractional residual functions and fractional Taylor expansions to obtain values of the coefficients of the fractional power series. To validate the efficiency and the applicability of our proposed approach we derive solutions of the fuzzy fractional initial value problem by testing two attractive applications. The compatibility of the behavior of the solutions is determined via some graphical and numerical analysis of the proposed results. Moreover, the comparative results point out that the proposed method is more accurate compared to the other existing methods. Finally, the results attained in this article emphasize that the residual power series technique is easy, efficient, and fast for predicting solutions of the uncertain models arising in real physical phenomena.

show abstract

Section: Preliminariesmentioning

confidence: 99%

Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense

Bataineh

Alaroud

Al‐Omari

et al. 2021

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the other hand, there are a lot of contributions related to solving systems of FDEs and since the nding of the analytical solution for a system of FDEs sometimes required a complex computation, analytical, and numerical techniques were established and developed to search for solutions of linear and nonlinear FDEs, see [26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we employ the ARA-RPS method to investigate analytical and approximate solutions of linear and nonlinear systems of FDEs. e ARA-RPS technique that has been introduced in [39] is a combination of the ARA transform [37][38][39] and the residual power series method [40][41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Qazza

Burqan

Saadeh

2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this research, systems of linear and nonlinear differential equations of fractional order are solved analytically using the novel interesting method: ARA- Residual Power Series (ARA-RPS) technique. This approach technique is based on the combination of the residual power series scheme with the ARA transform to establish analytical approximate solutions in a fast convergent series representation using the concept of the limit. The proposed method needs less time and effort compared with the residual power series technique. To prove the simplicity, applicability, and reliability of the presented method, three numerical examples are proposed and simulated. The obtained results show that the ARA-RPS technique is applicable, simple, and effective to get solutions to linear and nonlinear engineering and physical problems.

show abstract

“…due to that reason, several researchers have gained interest in it. Thereafter, Khalil et al [27] in 2021 have studied long-wave equations, Modanli et al [13] in 2020 have studied pseudo hyperbolic dierential equation, Kumar et al [28] in 2021 have discussed the bi-Hamiltonian Boussinesq System.…”

Section: Introductionmentioning

confidence: 99%

Semi-analytic solution of time-fractional Korteweg-de Vries equation using fractional residual power series method

Khirsariya

Rao

Chauhan

2022

Results in Nonlinear Analysis

View full text Add to dashboard Cite

In this paper, we have solved the non-linear Korteweg-de Vries equation by considering it in time-fraction Caputo sense and offered intrinsic properties of solitary waves. The fractional residual power series method is used to obtain the approximate solution of the aforesaid equation and compared the obtained results with Adomian Decomposition Method. Obtained results are efficient, reliable, and simple to execute on most of the non-linear fractional partial differential equations, which arise in various dynamical systems.

show abstract

Application of Laplace residual power series method for approximate solutions of fractional IVP’s

Cited by 34 publications

References 37 publications

Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense

Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense

Application of ARA-Residual Power Series Method in Solving Systems of Fractional Differential Equations

Semi-analytic solution of time-fractional Korteweg-de Vries equation using fractional residual power series method

Contact Info

Product

Resources

About