In this paper, alternative variational iteration method (AVIM) is presented to solve linear and nonlinear delay differential equations (DDEs). A general lagrange multiplier is used to construct a correction functional. The proposed series solutions are found to converge to exact solution rapidly. The computation of three test examples of DDEs was presented to confirm the efficacy and validity of AVIM. The results obtained show that the AVIM is very simple and efficient.
In the current paper, the concept of one-dimensional Shehu Transform have been generalized into three-dimensional Shehu Transform namely, Triple Shehu Transform (TRHT). Further, some main properties, several theorems and properties related to the TRHT have been established. Triple Shehu transform was used in solving fractional partial differential equations, with the fractional derivative described in Caputo sense. The proposed scheme finds the solution without any discretization, transformation or restrictive assumptions. Several examples are given to check the reliability and efficiency of the proposed technique.
In this paper, we suggest and analyze a technique by combining the Shehu transform method and the homotopy perturbation method. This method is called the Shehu transform homotopy method (STHM). This method is used to solve the time-fractional partial differential equations (TFPDEs) with proportional delay. The fractional derivative is described in Caputo's sense. The solutions proposed in the series converge rapidly to the exact solution. Some examples are solved to show the STHM is easy to apply.
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