Sarwar, ShahzadAleem, MaryamImran, Muhammad AsjadAkgul, Ali2024-12-242024-12-2420240749-159X1098-2426https://doi.org/10.1002/num.22688https://hdl.handle.net/20.500.12604/5925This study carried out the free convective non-Newtonian fluid of Brinkman type flow near an upright plate moving with velocity f(t). A fractional order model for non-Newtonian fluid of Brinkman type flow is proposed. The time derivative in the proposed fractional flow model is considered by using the two types of fractional derivatives namely Caputo fractional derivative and Atangana-Baleanu fractional derivative. The system of conjugated fractional partial differential equations for the temperature theta, velocity u and concentration C are worked out by applying optimal homotopy asymptotic technique. The effectuate of tangible and fractional variables on the domains of velocity u, temperature theta and concentration C are envisioned graphically. The rate of heat and mass transfer in the form of Nu and Sh is also calculated for both fractional derivatives. The numerical results reveal the efficiency, reliability, significant features, and simple in computation with high accuracy of consider method for non-Newtonian fractional order fluid of Brinkman type flow. We ascertained that our results are in excellent agreement with the exact results.eninfo:eu-repo/semantics/closedAccessAtangana? Baleanu fractional modelCaputo fractional derivativefree convectionheat and mass transferoptimal homotopy asymptotic method (OHAM)semi analytical solutionsvertical platesArticle401Q1WOS:000592096800001Q12-s2.0-8509679076410.1002/num.22688