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Full-Text Articles in Physical Sciences and Mathematics
Boundary Value Problems For A Second-Order $(P,Q) $-Difference Equation With Integral Conditions, İlker Gençtürk
Boundary Value Problems For A Second-Order $(P,Q) $-Difference Equation With Integral Conditions, İlker Gençtürk
Turkish Journal of Mathematics
Our purpose in this paper is to obtain some new existence results of solutions for a boundary value problem for a $ (p,q) $-difference equations with integral conditions, by using fixed point theorems. Examples illustrating the main results are also presented.
On The Existence For Parametric Boundary Value Problems Of A Coupled System Of Nonlinear Fractional Hybrid Differential Equations, Yige Zhao, Yibing Sun
On The Existence For Parametric Boundary Value Problems Of A Coupled System Of Nonlinear Fractional Hybrid Differential Equations, Yige Zhao, Yibing Sun
Turkish Journal of Mathematics
In this paper, we consider the existence and uniqueness for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations. By the fixed point theorem in Banach algebra, an existence theorem for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations is given. Further, a uniqueness result for parametric boundary value problems of a coupled system of nonlinear fractional hybrid differential equations is proved due to Banach's contraction principle. Further, we give three examples to verify the main results.
A Matrix-Collocation Method For Solutions Of Singularly Perturbed Differential Equations Via Euler Polynomials, Deni̇z Elmaci, Şuayi̇p Yüzbaşi, Nurcan Baykuş Savaşaneri̇l
A Matrix-Collocation Method For Solutions Of Singularly Perturbed Differential Equations Via Euler Polynomials, Deni̇z Elmaci, Şuayi̇p Yüzbaşi, Nurcan Baykuş Savaşaneri̇l
Turkish Journal of Mathematics
In this paper, a matrix-collocation method which uses the Euler polynomials is introduced to find the approximate solutions of singularly perturbed two-point boundary-value problems (BVPs). A system of algebraic equations is obtained by converting the boundary value problem with the aid of the collocation points. After this algebraic system, the coefficients of the approximate solution are determined. This error analysis includes two theorems which consist of an upper bound of errors and an error estimation technique. The present method and error analysis are applied to three numerical examples of singularly perturbed two-point BVPs. Numerical examples and comparisons with other methods …