A numerical approach for solving variable order differential equations based on Bernstein polynomials

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

Download Full-text

Unsteady hybrid-nanofluid flow comprising ferrousoxide and CNTs through porous horizontal channel with dilating/squeezing walls

Scientific Reports ◽

10.1038/s41598-021-91188-1 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Muhammad Bilal ◽

Hamna Arshad ◽

Muhammad Ramzan ◽

Zahir Shah ◽

Poom Kumam

Keyword(s):

Carbon Nanotubes ◽

Differential Equations ◽

Numerical Approach ◽

Hybrid Nanofluid ◽

Multi Wall Carbon Nanotubes ◽

Porous Walls ◽

Industrial Cleaning ◽

Energy Equations ◽

Single Wall Nanotubes ◽

Order Four

AbstractThe key objective of the present research is to examine the hybrid magnetohydrodynamics (MHD) nanofluid (Carbon-nanotubes and ferrous oxide–water) CNT–Fe3O4/H2 flow into a horizontal parallel channel with thermal radiation through squeezing and dilating porous walls. The parting motion is triggered by the porous walls of the channel. The fluid flow is time-dependent and laminar. The channel is asymmetric and the upper and lower walls are distinct in temperature and are porous. With the combination of nanoparticles of Fe3O4 and single and multi-wall carbon nanotubes, the hybrid nanofluid principle is exploited. By using the similarity transformation, the set of partial differential equations (PDEs) of this mathematical model, governed by momentum and energy equations, is reduced to corresponding ordinary differential equations (ODEs). A very simple numerical approach called the Runge–Kutta system of order four along with the shooting technique is used to achieve the solutions for regulating ODEs. MATLAB computing software is used to create temperature and velocity profile graphs for various emerging parameters. At the end of the manuscript, the main conclusions are summarized. Through different graphs, it is observed that hybrid-nanofluid has more prominent thermal enhancement than simple nanofluid. Further, the single-wall nanotubes have dominated impact on temperature than the multi-wall carbon nanotubes. From the calculations, it is also noted that Fe2O3–MWCNT–water has an average of 4.84% more rate of heat transfer than the Fe2O3–SWCNT–water. On the other hand, 8.27% more heat flow observed in Fe2O3–SWCNT–water than the simple nanofluid. Such study is very important in coolant circulation, inter-body fluid transportation, aerospace engineering, and industrial cleaning procedures, etc.

Download Full-text

Numerical solution of fractal-fractional Mittag–Leffler differential equations with variable-order using artificial neural networks

Engineering With Computers ◽

10.1007/s00366-020-01229-y ◽

2021 ◽

Author(s):

C. J. Zúñiga-Aguilar ◽

J. F. Gómez-Aguilar ◽

H. M. Romero-Ugalde ◽

R. F. Escobar-Jiménez ◽

G. Fernández-Anaya ◽

...

Keyword(s):

Neural Networks ◽

Artificial Neural Networks ◽

Differential Equations ◽

Numerical Solution ◽

Variable Order ◽

Artificial Neural

Download Full-text