Abstract
In this article, the iterative transformation method and homotopy perturbation transformation method are applied to calculate the solution of time-fractional Cauchy-reaction diffusion equations. In this technique, Shehu transformation is combined of the iteration and the homotopy perturbation techniques. Four examples are examined to show validation and the efficacy of the present methods. The approximate solutions achieved by the suggested methods indicate that the approach is easy to apply to the given problems. Moreover, the solution in series form has the desire rate of convergence and provides closed-form solutions. It is noted that the procedure can be modified in other directions of fractional order problems. These solutions show that the current technique is very straightforward and helpful to perform in applied sciences.
Highlights
Fractional partial differential equation (FPDE) fundamental signification is well-known in different engineering fields
The new iterative transformation method (NITM) is a combination of Shehu transform and the new iterative approach that provides the solution in the form of convergent series in an easy way
Consider the general fractional partial differential equation solve to homotopy perturbation transform method (HPTM): Dδημðφ, ηÞ + Mμðφ, ηÞ + Nμðφ, ηÞ
Summary
Fractional partial differential equation (FPDE) fundamental signification is well-known in different engineering fields. The new iterative transformation method (NITM) is a combination of Shehu transform and the new iterative approach that provides the solution in the form of convergent series in an easy way Another technique is the homotopy perturbation transform method (HPTM) to some applicable fractional models arising in real-life problems. Applications of three fractional models are demonstrated, and the analytical and numerical simulations of the three fractional models are provided to bolster the efficiency, simplicity, and high accuracy of the HPTM Many researchers use this method to solve different fractionalorder partial differential equations, such as fractional order gas dynamic equation [21], convection-diffusion problems [22], and Klein-Gordon equations [23].
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