Mittag–Leffler collocation optimization method for studying a physical problem in fluid flow with fractional derivatives

Abstract

An efficient computational approach is presented to solve numerically a mathematical model of fractional order in a fluid. The proposed model describes the effects of variable heat flux, viscous dissipation, and the slip velocity on the viscous Casson flow and heat transfer due to an unsteady stretching sheet taking into account the influence of heat generation or absorption. A collocation method based on a summation of Mittag-Leffler functions is employed to convert the system of ODEs that describe the problem to a system of algebraic equations. This system is constructed as a constrained optimization problem and optimized to get the unknown coefficients. Error analysis of the approximation solution is studied. The influence of the parameters governing the flow and heat transfer such as unsteadiness parameter, slip velocity parameter, Casson parameter, local Eckert number, heat generation parameter, and the Prandtl number are discussed and presented through tables and graphs. Besides, the local skin-friction coefficient and the local Nusselt number at the stretching sheet are computed and discussed. Finally, the results show that the given procedure is an easy and efficient tool to investigate the solution of such fluid models.

Numerical treatment via the spectral collocation method for Casson-Williamson nanofluid flow due to a stretching sheet with slip conditions

“…Because of their frequent appearance in many applications in fluid mechanics, viscoelasticity, biology, physics, and engineering, PDEs have been the subject of many investigations [27]. As a result, the solutions of ODEs of physical relevance have received a lot of attention [28]. The spectral collocation method depending on the 3SCPs was used to solve the nonlinear system of ODEs that regulate the physical problem quantitatively.…”

Numerical Study of Thermal Radiation Phenomenon and Its Influence on Amelioration of the Heat Transfer Mechanism through MHD Non-Newtonian Casson Model

“…The linear and non-linear differential equations, the integral equations, and the integro-differential equations have all been solved using these polynomials [22]. This method is also widely used to explain the fractional diffusion equation [23], fractional-order integro-differential equations and others ( [24][25][26][27]). The key benefit of this strategy is that it can obtain correct results by using only a few terms from the series solution.…”

Solving an inverse nodal problem with Herglotz–Nevanlinna functions in boundary conditions using the second‐kind Chebyshev wavelets method

“…Apart from these, there are some studies in the literature about similar numerical techniques. [25][26][27][28][29][30][31][32][33] The rest of the work will continue as follows. In Section 2, we denote asymptotic forms of eigenvalues, nodal points, and lengths of (1) and ( 2) and prove the uniqueness theorems.…”

“…Akbarpoor et al 24 studied the BVP () and () with $$$ {\delta}_k=0,k=1,2,\dots, d,{\Delta}_l=0,l=2,3,\dots, D $$$, and $$$ {h}_0={H}_0=0 $$$ and used FCW and Chebyshev interpolation methods to get solution of inverse nodal problem in 2019. Apart from these, there are some studies in the literature about similar numerical techniques 25–33 . The rest of the work will continue as follows.…”