Closed-form solutions of stochastic KdV equation with generalized conformable derivatives

Soliman, Ahmed H.; Hyder, Abd‐Allah

doi:10.1088/1402-4896/ab8582

Cited by 17 publications

(10 citation statements)

References 31 publications

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“…(2) If ω(ϑ, ρ) = ϑ 1-ρ and μ = ν = 0, then the Caputo LIFD and RIFD in (47) and (48) coincide with the left and right Caputo modifications of fractional derivatives defined by Jarad et al [30].…”

Section: Improved Fractional Derivatives In the Caputo Sensementioning

confidence: 96%

Novel improved fractional operators and their scientific applications

Hyder

Barakat

2021

Adv Differ Equ

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The motivation of this research is to introduce some new fractional operators called “the improved fractional (IF) operators”. The originality of these fractional operators comes from the fact that they repeat the method on general forms of conformable integration and differentiation rather than on the traditional ones. Hence the convolution kernels correlating with the IF operators are served in conformable abstract forms. This extends the scientific application scope of their fractional calculus. Also, some results are acquired to guarantee that the IF operators have advantages analogous to the familiar fractional integral and differential operators. To unveil the inverse and composition properties of the IF operators, certain function spaces with their characterizations are presented and analyzed. Moreover, it is remarkable that the IF operators generalize some fractional and conformable operators proposed in abundant preceding works. As scientific applications, the resistor–capacitor electrical circuits are analyzed under some IF operators. In the case of constant and periodic sources, this results in novel voltage forms. In addition, the overall influence of the IF operators on voltage behavior is graphically simulated for certain selected fractional and conformable parameter values. From the standpoint of computation, the usage of new IF operators is not limited to electrical circuits; they could also be useful in solving scientific or engineering problems.

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Section: Improved Fractional Derivatives In the Caputo Sensementioning

confidence: 96%

Novel improved fractional operators and their scientific applications

Hyder

Barakat

2021

Adv Differ Equ

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“…Previous studies have employed stochastic nonlinear Schrödinger equations to describe the behavior of stochastic optical solitons in nonlinear media. These equations have been extensively discussed in literature, with references such as [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

Shehab,

El‐Sheikh,

Ahmed

et al. 2023

Math Methods in App Sciences

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The improved modified extended tanh‐function approach was used to study optical stochastic soliton solutions and other exact stochastic solutions for the nonlinear Schrödinger‐Hirota equation with multiplicative white noise. The derived solutions include stochastic bright solitons, stochastic singular solitons, stochastic periodic solutions, stochastic singular periodic solutions, stochastic exponential solutions, stochastic rational solutions, and stochastic Jacobi elliptic doubly periodic solutions. Constraints on the parameters were taken into account to ensure the existence of the obtained stochastic soliton solutions. Additionally, selected solutions were presented graphically to illustrate the physical characteristics of the stochastic solutions. In this paper, we used Mathematica (11.3) packages to find the coefficients and Matlab (R2015a) packages to plot the graphs.

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“…Through the last two decennium, the stochastic KdV equation has been inspected hypothetically by many authors. [4][5][6][7][8] The checking of accurate and rough solutions of nonlinear development conditions plays a critical activity in the investigation of nonlinear physical questions. Numerous accommodating strategies, for example, bilinear change strategy, 9 the adjusted Clarkson and Kruskal (CK) direct strategy, 10 the multiscale extension strategy, 11 the binary Bell polyno-mials strategy, 12 the Riemann-Hilbert strategy, 13 the surmised balance strategy, 14 and the overall improved Kudryashov strategy 15 have been introduced in the ongoing writing.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, stochastic commotion is regularly thought of as a reliable instrument for stimulating the examination of the nonlinear dynamical models, by the additional mixing of hubbub, and, in some inquisitive sense, to assemble the force of the model, by discarding possibly useless solutions. Through the last two decennium, the stochastic KdV equation has been inspected hypothetically by many authors 4‐8 …”

Section: Introductionmentioning

confidence: 99%

Analytical manner for abundant stochastic wave solutions of extended KdV equation with conformable differential operators

Hyder

Soliman

2021

Math Methods in App Sciences

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This work investigates the Wick‐type stochastic and extended Korteweg‐de Vries (EKdV) equation under conformable differential operators. Novel wave solutions with soliton and periodic types are produced to the deterministic EKdV under conformable differential operators. Abundant stochastic wave solutions are explored for the Wick‐type stochastic EKdV equation by using conformable differential operators and the inverse Hermite transform. The stochastic soliton and periodic solutions are denoted as functional solutions with Brownian motion environment. For the acquired solutions, comparisons and graphical representations with three‐dimensional graphs are shown for peculiar values of the existing parameters. According to the existing literature, utilization of the conformable differential operators is a novel contribution for solving the stochastic EKDV and other stochastic nonlinear problems.

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Closed-form solutions of stochastic KdV equation with generalized conformable derivatives

Cited by 17 publications

References 31 publications

Novel improved fractional operators and their scientific applications

Novel improved fractional operators and their scientific applications

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

Analytical manner for abundant stochastic wave solutions of extended KdV equation with conformable differential operators

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