Solutions of fractional differential equations by using a blend of variational iteration method with Sumudu transform and application to price adjustment equations

Abstract

The presence of delays in a mathematical model can improve its vitality and suitability in describing several phenomena. However, in the presence of delays, nonlinear fractional differential equations are more difficult to study. This paper presents the use of a blend of variational iteration method with Sumudu transform for solving delay differential equations with Caputo derivatives of fractional variable order. Moreover, the paper introduces delays into the price adjustment equations to propose new price adjustment models with more potential for vitality and suitability. The paper assigns suitable real values to the parameters for the graphical display and comparison of the obtained solutions. The paper presents the interactions that exist among the price, demand, supply and dependence of supply and demand on the price, which can be applied to estimate the equilibrium price.

Keywords

• Sumudu transform
• Caputo fractional derivative
• Price adjustment
• Model
• Market equilibrium