New Implementation of Residual Power Series for Solving Fuzzy Fractional Riccati Equation

This paper reveals a computational method using a Residual Power Series Method (RPSM) for the solution of fuzzy fractional riccati equation under caputo fractional differentiability. An analytical solution of fuzzy fractional riccati equation is obtained as a convergent fractional power series. The procedure produces solutions of high accuracy, and some illustrative examples are solved with a different value of orders to show the efficiency of the RPSM

Design of neuro-computing paradigms for nonlinear nanofluidic systems of MHD Jeffery–Hamel flow

© 2018 Taiwan Institute of Chemical Engineers In this paper, a neuro-heuristic technique by incorporating artificial neural network models (NNMs) optimized with sequential quadratic programming (SQP) is proposed to solve the dynamics of nanofluidics system based on magneto-hydrodynamic (MHD) Jeffery–Hamel (JHF) problem involving nano-meterials. Original partial differential equations associated with MHD–JHF are transformed into third order ordinary differential equations based model. Furthermore, the transformed system has been implemented by the differential equation NNMs (DE-NNMs) which are constructed by a defined error function using log-sigmoid, radial basis and tan-sigmoid windowing kernels. The parameters of DE-NNM of nanofluidics system are optimized with SQP algorithm. To illustrate the performance of the proposed system, MHD–JHF models with base-fluid water mixed with alumina, silver and copper nanoparticles for different Hartman numbers, Reynolds numbers, angles of the channel and volume fractions with three different proposed DE-NNMs are designed to evaluate. For comparison purpose, the proposed results with reference numerical solutions of Adams solver illustrate their worth. Statistical inferences through different performance indices are given to demostrate the accuracy, stability and robustness of the stochastic solvers