Controlled Picard's Transform Technique for Solving a Type of Time Fractional Navier–Stokes Equation Resulting from Incompressible Fluid Flow

Fareed, Aisha F.; Elsisy, M. A.; Semary, Mourad S.; Elbarawy, Menna T. M. M.

doi:10.1007/s40819-022-01361-x

Cited by 6 publications

(2 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We acquire a positive integer j (shown in Equation ( 8)) by looking for the homogeneous balance between the predominant nonlinear component and the largest order derivative in Equation (7). 4. We next substitute (8) into (7) or the equation obtained by integrating (7), and lastly we arrange all the terms of U(χ) in the same order, yielding a polynomial in U(χ).…”

Section: The Working Procedures Of Medammentioning

confidence: 99%

“…These equations are significant because they represent complicated behaviors that are not captured by standard integer-order Nonlinear Partial Differential Equation (NPDEs). For example, in fluid dynamics, the Navier-Stokes equations expanded to include fractional derivatives that can more properly represent non-Newtonian fluid flow [4]. In biology, fractional FPDEs have been used to simulate the spread of illnesses with abnormal diffusion patterns [5].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solitary Waves Propagation Analysis in Nonlinear Dynamical System of Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation

Al-Sawalha,

Mukhtar,

Shah

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

The primary goal of this study is to create and characterise solitary wave solutions for the conformable Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equations (FCBWBKEs), a model that governs shallow water waves. Through wave transformations and the chain rule, the authors used the modified Extended Direct Algebraic Method (mEDAM) for transforming FCBWBKEs into a more manageable Nonlinear Ordinary Differential Equation (NODE). This accomplishment is particularly noteworthy because it surpasses the drawbacks linked to both the Caputo and Riemann–Liouville definitions in complying to the chain rule. The study uses visual representations such as 3D, 2D, and contour graphs to demonstrate the dynamic nature of solitary wave solutions. Furthermore, the investigation of diverse wave phenomena such as kinks, shock waves, periodic waves, and bell-shaped kink waves highlights the range of knowledge obtained in the study of shallow water wave behavior. Overall, this study introduces novel methodologies that produce valuable and consistent results for the problem under consideration.

show abstract

Section: The Working Procedures Of Medammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solitary Waves Propagation Analysis in Nonlinear Dynamical System of Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation

Al-Sawalha,

Mukhtar,

Shah

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

show abstract

On the soliton-type and other physical solutions for the space–time fractional Kraenkel–Manna–Merle model

Alhejaili,

Shah,

Salas

et al. 2024

Pramana - J Phys

View full text Add to dashboard Cite

Fractional discrete Temimi–Ansari method with singular and nonsingular operators: applications to electrical circuits

2023

View full text Add to dashboard Cite

The goal of this article is to present a recently developed numerical approach for solving fractional stochastic differential equations with a singular Caputo kernel and a nonsingular Caputo–Fabrizio and Atangana–Baleanu (ABC) kernel. The proposed method is based on the discrete Temimi–Ansari method, which is combined with three different numerical schemes that are appropriate for the new fractional derivative operators. The proposed technique is used to investigate the effects of Gaussian white-noise and Gaussian colored-noise perturbations on the potential source and resistance in fractional stochastic electrical circuits. The proposed method’s robustness and efficiency were demonstrated by comparing its results to those of the stochastic Runge–Kutta method (SRK). The valuable point in this article is that the resulting numerical scheme is able to combine two powerful methods that can be extended into more complex stochastic models. The comparison of different fractional derivatives using Mathematica 12 software has been obtained and the simulation results demonstrate the merit of the contributed method.

show abstract

Controlled Picard's Transform Technique for Solving a Type of Time Fractional Navier–Stokes Equation Resulting from Incompressible Fluid Flow

Cited by 6 publications

References 23 publications

Solitary Waves Propagation Analysis in Nonlinear Dynamical System of Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation

Solitary Waves Propagation Analysis in Nonlinear Dynamical System of Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation

On the soliton-type and other physical solutions for the space–time fractional Kraenkel–Manna–Merle model

Fractional discrete Temimi–Ansari method with singular and nonsingular operators: applications to electrical circuits

Contact Info

Product

Resources

About