The purpose of the study is to consider and measure the intellectual capital towards the financial performances of the local banks in Malaysia. The study will implement the Value Added Intellectual Coefficient (VAIC) method to evaluate the financial performances of the ten local banks in Malaysia. The study will determine how the intellectual capital influences the financial performances of banks in terms of two periods which are latest six years from 2011 to 2016 and the past ten years from 2007 to 2016. The regression analysis results to indicate that the components of intellectual capital have their influences towards the bank’s financial performances indicators. Over the six years and ten years periods, Capital Employed Efficiency has the significant relationship on Return on Assets. For the Return on Equity, Human Capital Efficiency (HCE) has the significant relationship over the latest six years while Structural Capital Efficiency (SCE) has the significant relationship over the ten years. Then, SCE has the significant relationship towards the Leverage (LEV) for the latest six years compare to the past ten years whereby HCE has the significant relationship towards the LEV. These results determine that the banks need to focus on the three components of intellectual capital whereby all the three efficiencies have the influences to enhance the best financial performances in Malaysia’s banking sector.

A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.

The homotopy perturbation method, Sumudu transform, and He’s polynomials are combined to obtain the solution of fractional Black-Scholes equation. The fractional derivative is considered in Caputo sense. Further, the same equation is solved by homotopy Laplace transform perturbation method. The results obtained by the two methods are in agreement. The approximate analytical solution of Black-Scholes is calculated in the form of a convergence power series with easily computable components. Some illustrative examples are presented to explain the efficiency and simplicity of the proposed method.