• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.1
• /
• pp.53-67
• /
• 2022

Nonlinear system of initial value problems involving R-L fractional derivative is studied. Monotone iterative technique coupled with lower and upper solutions is developed for the problem. It is successfully applied to study qualitative properties of solutions of nonlinear system of initial value problem when the function on the right hand side is nondecreasing.

• Kyungpook Mathematical Journal
• /
• v.54 no.3
• /
• pp.349-363
• /
• 2014

In this paper, we shall utilize Nevanlinna value distribution theory to study the uniqueness problems on entire functions and differential polynomials sharing one value. Our theorems improve or generalize some results of Zhang and Lin, Chen, Zhang, Lin and Chen.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.17 no.4
• /
• pp.221-237
• /
• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.711-721
• /
• 2010

Values of the parameter $\lambda$ are determined for which there exist positive solutions of the system of boundary value problems, $u^{(n)}+{\lambda}p(t)f(\upsilon)=0$, $\upsilon^{(n)}+{\lambda}q(t)g(u)=0$, for $t\;{\in}\;[a,b]$, and satisfying, $u^{(i)}(a)=0$, $u^{(\alpha)}(b)=0$, $\upsilon^{(i)}(a)=0$, $\upsilon^{(\alpha)}(b)=0$, for $0\;{\leq}\;i\;{\leq}\;n-2$ and $1\;{\leq}\;\alpha\;\leq\;n-1$ (but fixed). A well-known Guo-Krasnosel'skii fixed point theorem is applied.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.933-947
• /
• 2022

In this research, we presented the type 2 fuzzy transportation problem with additional constraints and solved by our proposed genetic algorithm model, and the results are verified using the softwares, genetic algorithm tool in Matlab and Lingo. The goal of our approach is to minimize the cost in solving a transportation problem with an additional constraint (TPAC) using the genetic algorithm (GA) based type 2 fuzzy parameter. We reduced the type 2 fuzzy set (T₂FS) into a type 1 fuzzy set (T₁FS) using a critical value-based reduction method (CVRM). Also, we use the centroid method (CM) to obtain the corresponding crisp value for this reduced fuzzy set. To achieve the best solution, GA is applied to TPAC in type 2 fuzzy parameters. A real-life situation is considered to illustrate the method.

• Journal of applied mathematics & informatics
• /
• v.35 no.5_6
• /
• pp.551-563
• /
• 2017

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales $$u^{{\Delta}{\nabla}}(t)+a(t)f(t,u(t))=0,\;t{\in}(0,T),\;{\beta}u(0)-{\gamma}u^{\Delta}(0)=0,\;u(T)={\sum_{i=1}^{m-2}}\;a_iu({\xi}_i),\;m{\geq}3$$, where $a(t){\in}C_{ld}((0,T),\;[0,+{\infty}))$, $f{\in}C([0,T]{\times}[0,+{\infty}),\;(-{\infty},+{\infty}))$, the nonlinear term f is allowed to change sign. We obtain several existence theorems of positive solutions for the above boundary value problems. In particular, our criteria generalize and improve some known results [15] and the obtained conditions are different from related literature [14]. As an application, an example to demonstrate our results is given.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1109-1118
• /
• 2009

In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.

• Journal of applied mathematics & informatics
• /
• v.7 no.1
• /
• pp.183-193
• /
• 2000

In this paper we use measure theory to solve a wide range of second-order boundary value ordinary differential equations. First, we transform the problem to a first order system of ordinary differential equations(ODE's)and then define an optimization problem related to it. The new problem in modified into one consisting of the minimization of a linear functional over a set of Radon measures; the optimal measure is then approximated by a finite combination of atomic measures and the problem converted approximatly to a finite-dimensional linear programming problem. The solution to this problem is used to construct the approximate solution of the original problem. Finally we get the error functional E(we define in this paper) for the approximate solution of the ODE's problem.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1265-1277
• /
• 2009

In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.

• Korean Journal of Mathematics
• /
• v.5 no.2
• /
• pp.211-215
• /
• 1997

In this paper, we introduce two notions of compactness defined by sequential convergence and compare them.