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Analysis of Time-Fractional \(\phi ^{4}\)-Equation with Singular and Non-Singular Kernels

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Abstract

In this article, we investigate the nonlinear time-fractional \(\phi ^{4}\)-equation under Caputo, Caputo-Fabrizio, and Atangana-Baleanu in Caputo’s sense. The modified double Laplace decomposition method is applied to study the proposed model under the aforementioned operators. The suggested approach is the combination of double Laplace and decomposition methods. It is observed that, the obtained series solutions of the system with considered fractional derivatives converges to the exact solution. A numerical example is presented with corresponding numerical simulations to demonstrate and validate the efficiency of the proposed technique. The error analysis of the considered equation with all considered operators is presented in the form of the tables. The physical behaviors of the obtained solutions with different fractional orders are discussed in detail.

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Data Availibility Statement

The data that support the findings of this study are available from the corresponding author.

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  1. Department of Mathematics, University of Malakand Chakdara Dir(L) KP Pakistan, Chakdara, Pakistan

    Fazlur Rahman, Amir Ali & Sayed Saifullah

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  1. Fazlur Rahman
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  2. Amir Ali
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Rahman, F., Ali, A. & Saifullah, S. Analysis of Time-Fractional \(\phi ^{4}\)-Equation with Singular and Non-Singular Kernels. Int. J. Appl. Comput. Math 7, 192 (2021). https://doi.org/10.1007/s40819-021-01128-w

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