On positive solutions of a nonlocal fractional boundary value problem
In this paper, we tend to investigate the existence and individualism of positive solutions for a nonlocal boundary price downside of fragmentary equation. Firstly, we tend to offer Green’s perform and prove its positivity; second, the distinctiveness of positive resolution is obtained by the employment of contraction map principle and a few Lipschitz-type conditions; third, by suggests that of the fastened purpose index theory, we tend to get some existence results of positive resolution. The proofs square measure based mostly upon the reduction of the matter thought-about to the equivalent Fredholm integral equation of second kind. [1]
A Nonlinear Singular Boundary Value Problem in the Theory of Pseudoplastic Fluids
The physical phenomenon equations for the category of non-Newtonian fluids termed pseudoplastic are examined beneath the classical conditions of uniform flow past a semi-infinite flat plate. The adoption of Crocco variables leads to a nonlinear, singular boundary worth drawback for the shear perform that is a motivating and natural generalization of the documented Crocco equation arising from the quality Newtonian fluid case. the individuality, existence and property of the answer are established and afterwards a definite series solution is exhibited. [2]
Boundary value problem for a coupled system of nonlinear fractional differential equations
In this work we have a tendency to discuss a boundary worth downside for a coupled differential system of fragmental order. The differential operator is taken within the Riemann–Liouville sense and also the nonlinear term depends on the fragmental by-product of Associate in Nursing unknown operate. By suggests that of Schauder fixed-point theorem, Associate in Nursing existence result for the answer is obtained. Our analysis depends on the reduction of the matter thought of to the equivalent system of Fredholm integral equations. [3]
On the Stability of MHD Boundary Layer Flow over a Stretching/Shrinking Wedge
The steady 2 dimensional magnetohydrodynamic (MHD) physical phenomenon flow and warmth transfer over a stretching/shrinking leaky wedge is numerically investigated. The partial differential equations governing the flow and warmth transfer are remodeled into a system of normal differential equations employing a similarity transformation. These equations are then solved numerically exploitation the boundary price convergent thinker, bvp4c in Matlab package. it’s found that twin solutions exist for a definite vary of the shrinking strength. A stability analysis is performed to spot that answer is stable and physically reliable. [4]
Solving Different Order Boundary Value Problems by Applying Homotopy Type Methods
In this manuscript, the strategies, optimum Homotopy straight line methodology (OHAM), Homotopy Perturbation methodology (HPM) and Homotopy Analysis methodology (HAM) ar applied to unravel varied order boundary worth issues. These techniques offer solutions within the sort of a series. Their solutions and graphs ar compared with their actual solutions and graphs. of these offer profitable results, however the optimum Homotopy straight line methodology is a lot of precise, whose convergence is restrained optimizations and therefore the convergence space is accustomed affording to the matter involved. The results show that the steered theme is a lot of active and relaxed to routine. [5]
Reference
[1] Bai, Z., 2010. On positive solutions of a nonlocal fractional boundary value problem. Nonlinear Analysis: Theory, Methods & Applications, 72(2), (Web Link)
[2] Nachman, A. and Callegari, A., 1980. A nonlinear singular boundary value problem in the theory of pseudoplastic fluids. SIAM Journal on Applied Mathematics, 38(2), (Web Link)
[3] Su, X., 2009. Boundary value problem for a coupled system of nonlinear fractional differential equations. Applied Mathematics Letters, 22(1), (Web Link)
[4] On the Stability of MHD Boundary Layer Flow over a Stretching/Shrinking Wedge
Izyan Syazana Awaludin, Anuar Ishak & Ioan Pop
Scientific Reportsvolume 8, Article number: 13622 (2018) (Web Link)
[5] Naeem, M., Khan, Z., Muhammad, S., Khan, L. and Uddin, J. (2018) “Solving Different Order Boundary Value Problems by Applying Homotopy Type Methods”, Journal of Advances in Mathematics and Computer Science, 28(2), (Web Link)