摘要:
The objective of this article is to explore the unsteady natural convection flows of Prabhakar-like non integer Maxwell fluid. Moreover, wall slip condition on temperature and Newtonian effects on heating are also studied. The generalized memory effects are illustrated with fractional time Prabhakar derivative. Dimensionless temperature and velocity are calculated analytically with the help of Laplace transform technique. A comparison among Prabhakar fractional natural convection flows and classical thermal transport which, illustrated by the Fourier's law. As a limiting case, we recovered the solution of ordinary Maxwell and Newtonian fluids from fractional Maxwell fluids with slip and no slip conditions. The results of fractional and important physical parameters are graphically covered. Accordingly, by comparing Maxwell fluids to viscous fluids, we found out that Maxwell fluids are move rapidly than viscous fluids. Moreover, the ordinary fluids moving fast than fractional fluids.
作者机构:
[Wang, Miao-Kun] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China.;[Chu, Hong-Hu] Hunan Univ, Coll Civil Engn, Changsha 410082, Hunan, Peoples R China.;[Chu, Yu-Ming] Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.
通讯机构:
[Yu-Ming Chu] C;College of Science, Hunan City University, Yiyang, China
关键词:
Gaussian hypergeometric function;Ramanujan's cubic transformation;Ramanujan's generalized modular equation;Generalized Grotzsch ring function
摘要:
We study several special functions in Ramanujan’s generalized modular equation with signature 3. Some sharp inequalities for these functions, including the estimates for the solution of Ramanujan’s generalized modular equation with signature 3 and triplication inequality for the generalized Grötzsch ring function with two parameters, are derived.
摘要:
In this paper, we have established a new identity related to Katugampola fractional integrals which generalize the results given by Topul et al. and Sarikaya and Budak. To obtain our main results, we assume that the absolute value of the derivative of the considered function φ' is p-convex. We derive several parameterized generalized Hermite-Hadamard inequalities by using the obtained equation. More new inequalities can be presented by taking special parameter values for λ, μ and p. Also, we provide two examples to illustrate our results.
期刊:
Journal of Computational Analysis and Applications,2020年28(3):560-566 ISSN:1521-1398
通讯作者:
Chu, Y.-M.
作者机构:
College of Science, Hunan City University, Yiyang, Hunan 413000, China;School of Continuing Education, Huzhou Vocational and Technological College, Huzhou, Zhejiang 313000, China;Friedman Brain Institute, Icahn School of Medicine at Mount Sinai, New York, NY 10029, United States;Department of Mathematics, Huzhou University, Huzhou, 313000, China
通讯机构:
Department of Mathematics, Huzhou University, Huzhou, China
关键词:
Arithmetic mean;Geometric mean;Toader mean
摘要:
In the aritcle, we prove that the double inequalities αA(a, b)+(1−α)G(a, b) < T [A(a, b), G(a, b)] < βA(a, b) + (1 − β)G(a, b) and G[λa + (1 − λ)b, λb + (1 − λ)a] < T [A(a, b), G(a, b)] < G[µa + (1 − µ)b, µb + (1 − µ)a] hold for all a, b > 0 with a = b if and only if α ≤ 1/2, β ≥ 2/π, λ ≤ (1 − 1 − 4/π 2)/2 and µ ≥ 1/2 − √ 2/4 if α, β ∈ R and λ, µ ∈ (0, 1/2), and find new bounds for the complete elliptic integral E(r) = π/2 0 (1 − r 2 sin 2 θ) 1/2 dθ (0 < r < 1) of the second kind, where G(a, b) = √ ab, T (a, b) = 2 π/2 0 a 2 cos 2 θ + b 2 sin 2 θdθ/π and A(a, b) = (a + b)/2 are respectively the geometric, Toader and arithmetic means of a and b.
作者机构:
[Liu, Hean] Hunan City Univ, Coll Sci, Yiyang 413000, Hunan, Peoples R China.;[Liu, Hean; Ki, Kim Yong] Sehan Univ, Grad Sch, Mokpo 58613, South Korea.
通讯机构:
[Liu, Hean] H;Hunan City Univ, Coll Sci, Yiyang 413000, Hunan, Peoples R China.
作者:
YING-QING SONG;YU-MING CHU;MUHAMMAD ADIL KHAN;ARSHAD IQBAL
期刊:
Journal of Computational Analysis and Applications,2020年28(4):685-697 ISSN:1521-1398
通讯作者:
Chu, Y.-M.
作者机构:
Department of Mathematics, Huzhou University, Huzhou 313000, China;College of Science, Hunan City University, Yiyang 413000, China;Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
通讯机构:
Department of Mathematics, Huzhou University, Huzhou, China
期刊:
Journal of Computational Analysis and Applications,2020年28(4):646-653 ISSN:1521-1398
作者机构:
Friedman Brain Institute, Icahn School of Medicine at Mount Sinai, New York, NY 10029,USA;College of Science, Hunan City University, Yiyang 413000, Hunan, China;Department of Mathematics, Huzhou University, Huzhou 313000, Zhejiang, China
摘要:
In the article, we prove that a = 3, β = log4/(π/2 - log 4)= 7.51371. ··· ,γ = 1/4 and δ = 1 + log2 - π/2 = 0.122351 ··? are the best possible constants such that the double inequalities hold for all r ∈ (0,1), where r' = √1-r~2, and K(r) = ∫_0~(π/2) dθ/√1-r~2sin~2θ and ε(r) =∫_0~(π/2)√1-r~2sin~2θdθ are the complete elliptic integrals of the first and second kinds.