http://jamda.abru.ac.ir/ Journal of Applied Mathematics & Data Analytics en daily 1 Fri, 01 May 2026 00:00:00 +0330 Fri, 01 May 2026 00:00:00 +0330 http://jamda.abru.ac.ir/article_736120.html Macroeconmic datasets has been analysed with various techniques. Traditional econometric approaches failed to capture cyclical and periodic structures in macroeconomic data, resulting in weak forecasts. This study addresses this gap by applying a Time Series Fourier Regression (TSFR) model to evaluate the impact of exchange rate fluctuations on Nigeria’s economic growth. Annual data on Gross Domestic Product (GDP) and official exchange rates from 1960 to 2023 were obtained from the Central Bank of Nigeria (CBN). The TSFR model was estimated using the Ordinary Least Squares (OLS) method and validated through the Durbin-Watson (DW) statistic, residual histograms, and Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) checks. Model performance was benchmarked against multiple regression, lagged regression and multiple Fourier regression models using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). It was revealed that exchange rate fluctuations significantly influence GDP. The TSFR model explained over 80% of GDP variability, with an adjusted coefficient of determination (R-squared) of 78%. Diagnostic tests confirmed normally distributed residuals without serial correlation. Comparative analysis demonstrated that the TSFR model consistently outperformed alternative models in terms of explanatory power and forecast accuracy. The results gives reliable insights into the dynamics between exchange rates and economic growth.The study establishes that Fourier-based time series models provide a superior framework for analysing macroeconomic data, effectively capturing both secular and cyclical movements. http://jamda.abru.ac.ir/article_736121.html In the present paper, we introduce a multi-quintic-sextic mapping as a system of functional equations taken from quintic and sextic functional equation. We describe the structure of such mappings and characterize them. In other words, we show that each multi-quintic-sextic mapping can be unified as a single equation. In the special cases, such mappings are multi-quintic and multi-sextic. Furthermore, by a classical direct (Hyers) method of stability, we establish the stability of multi-quintic-sextic mappings in the setting of Banach spaces. http://jamda.abru.ac.ir/article_736122.html The inflation rate in Nigeria has persistence, nonlinear exchange-rate effects, and large seasonal variations, making the forecasting of Nigeria’s inflation rate hard using standard linear time series models. Models of this type usually capture only one of the features and produce unstable forecasts and, importantly for developing economies, the impact of the exchange rate on inflation rate. A Fourier-Polynomial Time Series Regression (FP-TSR) model is proposed, which incorporates autoregressive dynamics, polynomial nonlinearity, interaction effects and Fourier components into a single framework. We analysed the monthly inflation and exchange rate data from the World Bank January 2004 to December 2024. Model parameters were estimated using ordinary least squares. Model fit was evaluated using the coefficient of determination ($R^2$) and adjusted $R^2$, while forecasting performance was assessed using root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results reveal strong inflation persistence and statistically significant nonlinear exchange-rate effects. The FP-TSR model achieves an $R^2$ of 0.933. In forecasting performance, it reduces RMSE, MAE, and MAPE by 1.41\%, 3.06\%, and 3.40\%, respectively, relative to the lagged regression model. These findings demonstrate consistent improvement in both explanatory power and predictive accuracy compared to polynomial, Fourier-only, and lagged regression models. The proposed model significantly improves inflation forecasting performance and provides a robust, policy-relevant tool for short-term inflation forecasting in Nigeria and offers a flexible structure for modelling macroeconomic time series exhibiting similar variation. http://jamda.abru.ac.ir/article_736123.html This paper extends our previous shape-parameter-free RBF-FD method [1] to the time-fractional Merton jump-diffusion model for pricing European put options. We retain the same spatial discretization: polyharmonic splines of the form r7 combined with complete polynomials up to degree 7 on local stencils of 101 nodes. Weights are computed once through a small augmented linear system. The Caputo fractional derivative (order α ∈ (0,1]) is discretized using the standard L1 scheme, while the jump integral is treated explicitly. To enhance accuracy near the strike price without much additional cost, we introduce a simple residual-based adaptive refinement: every ten time steps, nodes with high residual receive four additional Halton points nearby. Numerical tests on one-dimensional European puts show solid accuracy RMS errors usually between 10−5 and 10−8 for different α with clear convergence as the number of nodes increases. Compared to the non-fractional case and standard multiquadric RBF-FD (which needs shape-parameter tuning), our method is efficient and robust. It is easy to implement and extends naturally to higher dimensions. http://jamda.abru.ac.ir/article_736124.html In this paper, we investigate the existence and uniqueness of solutions for a nonlinear fractional differential equation involving the Riemann-Liouville fractional derivative of order $\vartheta \in (m-1, m]$. We construct the Green's function for the corresponding linear boundary value problem and analyze its properties. By employing the Banach contraction mapping principle, we establish sufficient conditions for the existence of a unique solution. A specific emphasis is placed on the structural differences between Riemann-Liouville and Caputo frameworks, particularly regarding the general solutions and the behavior of the Green's function integral bounds. http://jamda.abru.ac.ir/article_736125.html Divorce is a multi-stage process that affects both the relationships within a family and entangles the entire society in numerous problems. It is one of the fundamental harms and issues in society that causes the family unit to collapse. In recent years, divorce in Iran has been sharply increasing. This phenomenon significantly impacts the family and society. While economic factors are not the sole cause of divorce, they provide the groundwork for its occurrence. The effective economic factors include inflation, unemployment, per capita income, and the Gini coefficient or unequal distribution of per capita income. This study aims to investigate the economic roots of divorce in Iran. The present study investigates the economic roots of divorce in the provinces of Iran using a dynamic panel data model and the Generalized Method of Moments (GMM) over the period 2008–2018. The estimation results of the research model have shown that unemployment, inflation, and the Gini coefficient as an indicator of income inequality have an increasing effect on divorce, while an increase in per capita income has led to a decrease in divorce. Considering the increasing effects of unemployment, inflation, and income inequality on divorce, as well as the decreasing effect of per capita income on this social phenomenon, it is suggested to implement policies that strengthen economic growth, leading to higher per capita income and lower unemployment and inflation rates. Additionally, income redistribution policies, such as improving the tax system and the proper targeting of subsidies, should be employed to facilitate a reduction in divorce within Iranian society.