New fractional derivatives with non-singular kernel applied to the Burgers equation

2018 ◽  
Vol 28 (6) ◽  
pp. 063109 ◽  
Author(s):  
Khaled M. Saad ◽  
Abdon Atangana ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Derivatives ◽  
Burgers Equation ◽  
Singular Kernel

scholarly journals Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2326
Author(s):  
Noufe H. Aljahdaly ◽  
Ravi P. Agarwal ◽  
Rasool Shah ◽  
Thongchai Botmart
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Burgers Equation ◽  
Singular Kernel ◽  
Exact Results ◽  
Burgers Equations ◽  
Kernel Operators ◽  
Natural Decomposition

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed by inverse Natural transform, to achieve the result of the equations. To validate the method, we have considered a two examples and compared with the exact results.

scholarly journals Two Reliable Methods for The Solution of Fractional Coupled Burgers’ Equation Arising as a Model of Polydispersive Sedimentation

2019 ◽  
Vol 4 (2) ◽  
pp. 523-534 ◽  
Author(s):  
Ali Kurt ◽  
Mehmet Şenol ◽  
Orkun Tasbozan ◽  
Mehar Chand
Keyword(s):  
Water Waves ◽  
Fractional Derivatives ◽  
Burgers Equation ◽  
Approximate Solutions ◽  
Iteration Algorithm ◽  
Shallow Water Waves ◽  
Fractional Differential ◽  
Reliable Methods ◽  
Coupled Burgers Equation ◽  
Partial Fractional Differential Equations

AbstractIn this article, we attain new analytical solution sets for nonlinear time-fractional coupled Burgers’ equations which arise in polydispersive sedimentation in shallow water waves using exp-function method. Then we apply a semi-analytical method namely perturbation-iteration algorithm (PIA) to obtain some approximate solutions. These results are compared with obtained exact solutions by tables and surface plots. The fractional derivatives are evaluated in the conformable sense. The findings reveal that both methods are very effective and dependable for solving partial fractional differential equations.

Modeling electro-magneto-hydrodynamic of blood flow in multi-stenosed artery using fractional deivatives without singular kernel

2020 ◽  
Author(s):  
F. J. Dzuliana ◽  
Uddin Salah ◽  
Roslan Rozaini ◽  
Md Akhir Mohd Kamalrulzaman
Keyword(s):  
Blood Flow ◽  
Pressure Gradient ◽  
Fractional Derivatives ◽  
Magnetic Particles ◽  
Circulatory System ◽  
Singular Kernel ◽  
Electric And Magnetic Fields ◽  
Stenosed Artery ◽  
Flow Through ◽  
Common Problems

Stenosis is one of the most common problems in blood flow through arteries. Stenosis means narrowing arteries. Among the various cardiovascular diseases, stenosis is a major one that affects blood flow in the arteries and becomes the leading cause of death worldwide. Therefore, several studies were conducted either experimentally or mathematically to understand stenosis effects on blood flow through arteries. This study investigates the Newtonian fluid’s electro-magneto-hydrodynamic flow mixed with uniformly distributed magnetic particles through a multi-stenosed artery. The fluid is acted by an arbitrary timedependent pressure gradient, external electric and magnetic fields, and the porous medium. The governing equations are considered as fractional partial differential equations based on the Caputo–Fabrizio time-fractional derivatives without singular kernel. The fractional model of blood flow in the multi-stenosed artery will be presented subject to several external factors. These include the severity of the stenosis and the magnetic particles with the presence of an electromagnetic field. The steady and unsteady parts of the pressure gradient that give rise to the systolic and diastolic pressures are considered as the pumping action of the heart, which in turn produces a pressure gradient throughout the human circulatory system. The fractionaloperator’s effect and pertinent system parameters on blood flow axial velocities are presented and discussed for future works.

scholarly journals Fractional Variational Iteration Method and Its Application to Fractional Partial Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Iteration Method ◽  
Fractional Derivatives ◽  
Financial Models ◽  
Gordon Equation ◽  
Burgers Equation ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Liouville Derivative ◽  
Black Scholes ◽  
Klein Gordon

We use the fractional variational iteration method (FVIM) with modified Riemann-Liouville derivative to solve some equations in fluid mechanics and in financial models. The fractional derivatives are described in Riemann-Liouville sense. To show the efficiency of the considered method, some examples that include the fractional Klein-Gordon equation, fractional Burgers equation, and fractional Black-Scholes equation are investigated.

scholarly journals Optimal Perturbation Iteration Method for Solving Fractional Model of Damped Burgers’ Equation

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 958 ◽  
Author(s):  
Sinan Deniz ◽  
Ali Konuralp ◽  
Mnauel De la Sen
Keyword(s):  
Laplace Transform ◽  
Analytical Solutions ◽  
Differential Form ◽  
Fractional Derivatives ◽  
Burgers Equation ◽  
Optimal Perturbation ◽  
Fractional Differential ◽  
Fractional Type ◽  
Iteration Technique ◽  
Fractional Differential Form

The newly constructed optimal perturbation iteration procedure with Laplace transform is applied to obtain the new approximate semi-analytical solutions of the fractional type of damped Burgers’ equation. The classical damped Burgers’ equation is remodeled to fractional differential form via the Atangana–Baleanu fractional derivatives described with the help of the Mittag–Leffler function. To display the efficiency of the proposed optimal perturbation iteration technique, an extended example is deeply analyzed.

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