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- MakaleAçık Erişim2026Enhanced Computational Efficiency in Solving Delay Fractional Partial Differential Equations Through the Yang Decomposition Method
Ali, Mustafa Ahmed; Merdan, Mehmet
This study presents the Yang Transform Adomian Decomposition Method (YTADM), a semi-analytical framework for solving one-dimensional linear and nonlinear delay fractional partial differential equations involving the Caputo fractional derivative. The proposed method combines the Yang transform with the Adomian decomposition method to construct recursive solution series while efficiently handling delayed nonlinear terms. The applicability of the proposed framework is demonstrated through several examples, including proportional-delay Burgers-type equations, and its convergence properties are analyzed. The obtained results show that YTADM yields rapidly convergent semi-analytical approximations and provides an effective framework for solving one-dimensional delay fractional partial differential equations.
- MakaleYalnız künye2013A multistage variational iteration method for solution of delay differential equations
Gökdoǧan, Ahmet; Merdan, Mehmet; Ertürk, Vedat Suat
In this paper, the approximate solution of delay differential equations is obtained by a reliable algorithm based on an adaptation of the classical variational iteration method (VIM), which is called the multi-stage variational iteration method (MSVIM). Examples are carried out and numerical results with comparison to exact solutions, VIM and MATLAB dde23 solver are given. The comparison reveals that the MSVIM is a promising tool to solve delay differential equations.