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- MakaleAçık Erişim2026Scopus SJRQ3Solution of Time-Fractional Coupled Burgers Equations by the Yang Transform Adomian Decomposition Method
Ali, Mustafa Ahmed; Merdan, Mehmet
In this paper, the Yang transform Adomian decomposition method (YTADM) is employed in the solution of nonlinear time-fractional coupled Burgers equations. The technique solves the fractional and nonlinear terms successfully via the Adomian decomposition of the Yang transform. Illustrative examples are given, which show the accuracy and ease of implementation of the method. The results show that the YTADM method gives good, reliable results and is very accurate, so that its solutions agree well with the exact solution. Finally, tables and graphs are shown, which illustrate the behavior of the solutions found.
AtıfScopus2WoS1OpenAlex2İncele - MakaleAçık Erişim2026Scopus SJRQ2Enhanced 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.
- MakaleAçık Erişim2025Scopus SJRQ3Investigation of fractional order covid-19 model with q-homotopy analysis transform method
Merdan, Mehmet; Açikgöz, Pınar
The primary objective of this paper is to derive approximate analytic solutions for the time fractional-order Covid-19 model by employing the q-homotopy analysis transform method (q-HATM) and the Laplace transform homotopy perturbation method (LT-HPM). The covid 19 model is a system of five-dimensional nonlinear ordinary differential equations. Moreover, this method applies even to more complex partial differential equations originating from mathematical biology, demonstrating computational efficiency and wide application. In this study, Caputo fractional derivative is used to obtain the fractional system and Laplace transformation is applied to analyze the approximate solutions of the system. Graphical results are presented and discussed quantitatively to illustrate the approximate solution. Copyright 2021, Yıldız Technical University.
- MakaleAçık Erişim2025Scopus SJRQ2Investigation of Nonstandard Finite Difference for Fractional Order Covid-19 Model
Merdan, Mehmet; Acikgoz, Pınar
This article examines a mathematical model of the Covid-19 type. We demonstrate how the population is impacted by immigration, protection, the mortality, exposure, curing, and interactions between sick and healthy individuals. There are five classifications in our model: exposed, susceptible, infected, quarantined, and recovered. The model is subjected to numerical and fractional analysis in this instance. The numerical analysis is performed using the fractional order non-standard finite difference (NSFD) scheme. The Grunwald-Letnikov numerical approximation technique is used for fractional analysis. The findings are evaluated by simulations using the Matlab tool.
AtıfScopus3WoS2OpenAlex2İncele - MakaleAçık Erişim2024Scopus SJRQ2Approximate Solutions of Fractional Differential Equations Using Optimal q-Homotopy Analysis Method: A Case Study of Abel Differential Equations
Şengül, Süleyman; Bekiryazici, Zafer; Merdan, Mehmet
In this study, the optimal q-Homotopy Analysis Method (optimal q-HAM) has been used to investigate fractional Abel differential equations. This article is designed as a case study, where several forms of Abel equations, containing Bernoulli and Riccati equations, are given with ordinary derivatives and fractional derivatives in the Caputo sense to present the application of the method. The optimal q-HAM is an improved version of the Homotopy Analysis Method (HAM) and its modification q-HAM and focuses on finding the optimal value of the convergence parameters for a better approximation. Numerical applications are given where optimal values of the convergence control parameters are found. Additionally, the correspondence of the approximate solutions obtained for these optimal values and the exact or numerical solutions are shown with figures and tables. The results show that the optimal q-HAM improves the convergence of the approximate solutions obtained with the q-HAM. Approximate solutions obtained with the fractional Differential Transform Method, q-HAM and predictor–corrector method are also used to highlight the superiority of the optimal q-HAM. Analysis of the results from various methods points out that optimal q-HAM is a strong tool for the analysis of the approximate analytical solution in Abel-type differential equations. This approach can be used to analyze other fractional differential equations arising in mathematical investigations.
AtıfScopus4WoS5OpenAlex5İncele - MakaleAçık Erişim2020Solving for the random component time-fractional partial differential equations with the new Sumudu transform iterative method
Anaç, Halil; Merdan, Mehmet; Kesemen, Tülay
The new Sumudu transform iterative method is implemented to get the approximate solutions of random component time-fractional partial differential equations with Caputo derivative. The parameters and the initial conditions of the random component time-fractional partial differential equations are analyzed with Gamma distribution. The expected values and variances of these solutions are calculated, and the graphs of the expected values and variances are plotted in Maple software. The results for the random component time-fractional partial differential equations with Gamma distribution are examined to investigate effects of this distribution on results. The numerical experiments indicate that this method is very effective.
AtıfScopus12WoS11OpenAlex16İncele