Abstract
The aim of this paper is a new semianalytical technique called the variational iteration transform method for solving fractional-order diffusion equations. In the variational iteration technique, identifying of the Lagrange multiplier is an essential rule, and variational theory is commonly used for this purpose. The current technique has the edge over other methods as it does not need extra parameters and polynomials. The validity of the proposed method is verified by considering some numerical problems. The solution achieved has shown that the better accuracy of the proposed technique. This paper proposes a simpler method to calculate the multiplier using the Shehu transformation, making a valuable technique to researchers dealing with various linear and nonlinear problems.
Highlights
In the last decade, significant achievements have been made to applying and the theory of fractional differential equations (FDEs)
Significant achievements have been made to applying and the theory of fractional differential equations (FDEs). These problems are increasingly implemented to model equations in research fields as diverse as mechanical schemes, dynamical schemes, chaos, continuous-time random walks, control, chaos synchronization, subdiffusive systems and anomalous diffusive, wave propagation phenomena and unification of diffusion, and so on
Fractional-order schemes have become famous for this valuable property
Summary
Significant achievements have been made to applying and the theory of fractional differential equations (FDEs). These problems are increasingly implemented to model equations in research fields as diverse as mechanical schemes, dynamical schemes, chaos, continuous-time random walks, control, chaos synchronization, subdiffusive systems and anomalous diffusive, wave propagation phenomena and unification of diffusion, and so on. The benefits of the fractional-order scheme are that it allows more significant degrees of freedom in the problem. Fractional-order schemes have become famous for this valuable property. Another explanation for applying fractional-order derivatives is that they are naturally linked to memory structures that prevail in most physical and scientific structure models.
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