The present investigation suggests a novel control technique that merge the advantage of the adaptive Neuro-Fuzzy inference system (ANFIS) with the proportional integral derivative (PID) controller, abbreviated as (ANFIS-PID), for dealing with the dynamics of the of wheeled mobile robot (WMR). A comparative study of various meta-heuristic optimization algorithms is made. The results revealed the highest efficiency of the suggested ANFIS-PID technique compared to seven designed PID controllers, in terms of settling and rise time, overshoot, and the integral square error (ISE) as a cost function. Various cases, study (circular path, diamond path, zigzag path) have highlighted the over performance of mentioned controller. Moreover, this hybrid technique is fused with backstepping approach for the kinematic control. A lemniscate and a square trajectory were performed to clarify the capability of the mentioned controller.

A Haar wavelet collocation method (HWCM) is presented for the solution of Riccati equation subject to the two-point and integral boundary condition. The qua?silinearization technique is applied to linearized the Riccati equation and then the linearized equation with boundary condition is solved by converting into system of algebraic equation with the help of Haar wavelets. We have considered three different form of Reccati equation, two having integral boundary condition and one with two-point boundary condition. The numerical results obtained by HWCM are stable, efficient and convergent.

In this work, numerical solution of multi term space fractional PDE is calculated by using radial basis functions. The fractional derivatives of radial basis functions are evaluated by Caputo and Riemann-Liouville definitions. Local radial basis functions are applied to get stable and accurate solution the problem. Accuracy of the method is assessed by using double mesh procedure. Numerical solutions are presented for different fractional orders to show the effect of introducing fractionality.

In the present article, the fractional order differential difference equation is solved by using the residual power series method. Residual power series method solutions for classical and fractional order are obtained in a series form showing good accuracy of the method. Illustrative models are considered to affirm the legitimacy of the technique. The accuracy of the chosen problems is represented by tables and plots which show good accuracy between the exact and assimilated solutions of the models.

The natural streamflow of the River is encouraged to forecast through multiple methods. The impartiality of this study is the comparison of the forecast accuracy rates of the time-series (TS) hybrid model with the conventional model. The behavior of the natural monthly statistical chaotic streamflow to use in the forecasting models has been compiled by projecting two distinguished rivers, the Indus and Chenab of Pakistan. Therefore, this article is based on the monthly streamflow forecast analysis that has been reported using the group method of data handling with wavelet decomposition (WGMDH) as a new forecasting attribute. Discrete wavelets decompose the perceived data into sub-series and forecast hydrological variables; these fittingly have been endorsed as inputs in the hybrid model. The forecast efficiency and estimations of the hybrid model are measured by the appropriate statistical techniques such as mean absolute error (RME), root mean square error (RMSE), and correlation coefficients (R) and compared to the group method of data handling (GMDH), least-square support vector machine and artificial neural network conventional models. The comparative analysis shows that the hybrid WGMDH model is more stable and more potent for forecasting river flow than other predictive models and significantly proved that the hybrid model is a robust alternate forecasting tool for TS data sets.