sedaghat shahmorad

This paper is devoted to prove the existence of extremal solutions for multi-term nonlinear fractional differential equations with nonlinear boundary conditions. The fractional derivative is of Caputo type and the inhomogeneous term depends on the fractional derivatives of lower orders. By establishing a new comparison theorem and applying the monotone iterative technique, we show the existence of extremal solutions. The method is a constructive method that yields monotone sequences that converge to the extremal solutions. As an application, some examples are presented to illustrate the main results.

The conversion of rainfall to runoff in basins includes nonlinear relations between the complex interactions of various hydrological processes. In this study, without considering of predetermined structure, relationship between input and output system was derived individually from the nature of the data recorded. Also, the phase difference occurred between rainfall and runoff signals using cross-wavelet transform analysis. Then phase difference diagram was plotted for the single and compound events of Lighvan basin. By applying these phases at the time of the rainfall signals, all errors resulting from considering average losses in basin was minimized that in this study was introduced as "minimum error time position"(METP). Also, discharge forecasting for basin was carried out by Kalman filter model and optimization in Lighvan basin state space, using calibration step events. By applying this phase difference to effective rainfall components, the error resulting from the considering of average infiltration losses and φ index decreases to the minimum. Also, using the linear programming optimization method, the unit hydrograph for Lighvan basin was used as Kalman filter measurement model. The results showed that by applying the phases difference between rainfall and runoff signals and integration with Kalman filtering and linear programming (KF-LP-CW), the corrected Nash-Sutcliff coefficient were obtained 0.94 in both Calibration and verification steps. These values were obtained 0.63 and 0.68 in calibration and validation steps respectively, as compared to the state that phase difference was not applied (KF-LP method). Therefore, in this study, significant improvement was observed with the application of phase differences in effective precipitation components.

One of the main concerns of economic scholars and thinkers is to predict the behavior of individuals in an economic system. Although economists often use complex mathematical equations for economic analysis, in recent decades due to the weakness of forecasting analyses based on equations and inability of such equations to justify empirical events, economists have used modeling and simulation methods. In other words, they are Looking for ways to justify complex phenomena in the economy as a complex system. In addition to applying complexity theory, this research attempts to introduce a research tool to scholars for the simulation of agent-based research. In this study, we will examine the efficiency of each system by developing an agent-based model based on a No-Ponzi economic system and comparing it with a Ponzi economic model. We will also examine the effects and consequences of some economic behaviors that are contrary to the ethics and teachings of Islam. Comparing the two models, the results indicate that the No-Ponzi model has a better human development index and more social welfare.

Establishing social justice and equilibrium in society is one of the most important preconditions for development. Therefore, reducing the trend of increasing inequality for policymakers in many countries is a priority. Zakat is a financial tool in the macro system of Islamic society, which plays an important role in the effective allocation of income. The purpose of this article is to describe the theory of the role of zakat as an important tool in achieving efficiency and improving human development indicators. For this purpose, the Net Logo application has been used for agent-based modeling. This paper examines the actual effects of Zakat on the distribution of wealth in Islamic economics and compares conventional and Islamic economics. The results indicate that an Islamic economic system, in general, leads to higher human development indicators than a conventional investment model system. JEL Classification: C53, P4, D630, D310, E21

The existence of high uncertainty and the nonlinearity of rainfall and runoff relationships signalize the vacancy of many studies in this direction. The present study is conducted with the aim of simulating and predicting the watershed’s behavior based on the recognition of a part of the relationships prevailing on this complex system. In this study, Cross wavelet transform methods, Kalman Filter and Linear Programming (KF-LP_CW) were used to analysis of 9 compound events of rainfall and runoff in the Sufi Chai watershed with about 250.65 km2 area. Then, to compare the performance of this method, the results were compared with geomorphologic unit hydrograph combination with Cross wavelet (GIUH-CW) and geomorphologic unit hydrograph based on Nash models combination with Cross wavelet (GIUH-Nash-CW). Considering the satisfactory performance of all three models, the final performance of these methods was finally discussed using the evaluation criteria used in the research. Results showed that the KF-LP_CW method simulated the compound events in the calibration and validation stage with a mean square error (MSE) of 2.47 and 3.2, respectively. In the case of time to peak, the mean average relative error (MARE) for the three studied methods was 0.05 and 0.037 for the calibration and validation stages, respectively. The same criteria for peak discharge and base time were 0.07 and 0.06 respectively for the two calibration stages, and 0.18 and 0.07 in the two validation stages. This indicates better performance of the methods in the estimation of time to peak, base time, and peak discharge, respectively.

Hydrological modeling plays a valuable role in watershed management. In order to advance this important, in this study, a combination of linear programming, cross-wavelet transform and Kalman filter as a control model for the analysis of nine compound rainfall and runoff events were used in Sufi Chay Basin. The results were compared with modified time area unit hydrograph, and e geomorphologic unit hydrograph. Finally, using the evaluation criteria used in the research, the final performance of these methods was investigated and analyzed. it was revealed that the modified time area method has a relatively weaker performance than the other two methods, which is due to the assumptions used in drawing the isochrones lines. The LP-CW-KF method showed the best performance among the studied methods, which simulated the compound events in the calibration and validation stage with a mean squared error of 2.47 and 2.7, respectively. On average, in all the events and the three studied methods, the mean absolute relative error (MARE) was 0.069 in the time to peak, 0.131 in the peak discharge and 0.125 in the base time. Therefore, on average, all methods showed a better performance in estimating time to peak.

This study evaluates the performance of the linear first-order Volterra model for simulating nonlinear rainfall-runoff process. For this end, fifteen storm events over the Navrood River basin were collected. 70% and 30% of the events were used to calibrate and test the suitability of the model. Finally, the performance of the model was compared with the artificial neural networks (multilayer perceptron (MLP)) using five performance criteria namely coefficient of efficiency, root mean square error, error of total volume, relative error of peak discharge and error of time for peak to arrive. Results indicated that the intelligent MLP models outperformed the Volterra model. The linear Volterra model was not more effective in simulating the rainfall-runoff process. It needs to be extended to higher orders and also the number of the parameters should be reduced.

In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the proposed method.

This paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. Then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. Finally an example is given to illustrate the performance of the methods.