Abstract
This paper investigates a modified analytical method called the Adomian decomposition transform method for solving fractional-order heat equations with the help of the Caputo-Fabrizio operator. The Laplace transform and the Adomian decomposition method are implemented to obtain the result of the given models. The validity of the proposed method is verified by considering some numerical problems. The solution achieved has shown that the better accuracy of the suggested method. Furthermore, due to the straightforward implementation, the proposed method can solve other nonlinear fractional-order problems.
Highlights
The fractional generalization of differential equations has proven to be an effective and precise tool for interpreting real-world problems
The exact result of nonlinear equations plays a crucial role in deciding the characteristics and behavior of physical processes, but as dealing with linear equations, it is impossible to find their exact results
The results of heat equations have been used of many researcher of mathematics, such as the Adomian decomposition technique [15], the optimal homotopy asymptotic technique [16], the differential transform technique [17], the variational iteration technique [18], Bernstein polynomials with the operational matrix [19], the homotopy perturbation method (HPM) [20], apply the variational iteration technique and Yang-Laplace transformation of time-fractional heat equations [21], Elzaki transformation and the differential transformation technique for nonlinear wave equation [22], and the Aboodh decomposition method [23]
Summary
The fractional generalization of differential equations has proven to be an effective and precise tool for interpreting real-world problems. Fractional derivatives have mathematically interpreted many physical problems in recent decades; these representations have produced excellent solutions in real-world modeling issues. The results of heat equations have been used of many researcher of mathematics, such as the Adomian decomposition technique [15], the optimal homotopy asymptotic technique [16], the differential transform technique [17], the variational iteration technique [18], Bernstein polynomials with the operational matrix [19], the homotopy perturbation method (HPM) [20], apply the variational iteration technique and Yang-Laplace transformation of time-fractional heat equations [21], Elzaki transformation and the differential transformation technique for nonlinear wave equation [22], and the Aboodh decomposition method [23]. Multistep ADTM are applied to investigate fractional partial differential equations in [27].
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