Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Entire DC Network
Existence Results And Ulam-Hyers Stability To Impulsive Coupled System Fractional Differential Equations, Hadjer Belbali, Maamar Benbachir
Existence Results And Ulam-Hyers Stability To Impulsive Coupled System Fractional Differential Equations, Hadjer Belbali, Maamar Benbachir
Turkish Journal of Mathematics
In this paper, the existence and uniqueness of the solutions to impulsive coupled system of fractional differential equations with Caputo--Hadamard are investigated. Furthermore, Ulam's type stability of the proposed coupled system is studied. The approach is based on a Perov type fixed point theorem for contractions.
Solving Fractional Differential Equations Using Collocation Method Based On Hybrid Of Block-Pulse Functions And Taylor Polynomials, Yao Lu, Yinggan Tang
Solving Fractional Differential Equations Using Collocation Method Based On Hybrid Of Block-Pulse Functions And Taylor Polynomials, Yao Lu, Yinggan Tang
Turkish Journal of Mathematics
In this paper, a novel approach is proposed to solve fractional differential equations (FDEs) based on hybrid functions. The hybrid functions consist of block-pulse functions and Taylor polynomials. The exact formula for the Riemann--Liouville fractional integral of the hybrid functions is derived via Laplace transform. The FDE under consideration is converted into an algebraic equation with undetermined coefficients by using this formula. A set of linear or nonlinear equations are obtained through collocating the algebraic equation at Newton-Cotes nodes. The numerical solution of the FDE is achieved by solving the linear or nonlinear equations. Error analysis is performed on the …
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
By application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the Leray-Schauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411).