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Invariant subspaces and exact solutions: \((1+1)\) and \((2+1)\)-dimensional generalized time-fractional thin-film equations

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Abstract

We investigate the applicability and efficiency of the invariant subspace method to (2 + 1)-dimensional time-fractional nonlinear PDEs. We show how to find various types of invariant subspaces and reductions for the (1 + 1) and (2 + 1)-dimensional generalized nonlinear time-fractional thin-film equations which arise from the motion of liquid film on a solid surface under the influence of surface tension. We construct several kinds of exact solutions for the above-mentioned equations depending on arbitrary functions as either a combination of trigonometric, polynomial, Mittag–Leffler, and exponential type functions or any of these forms. Also, we demonstrate the applicability of the invariant subspace method to solve the initial and boundary value problem of nonlinear time-fractional PDEs for the first time and illustrate it through the physically important generalized time-fractional thin-film and linear time-fractional heat equations. Finally, we present some of the obtained exact solutions graphically.

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Authors and Affiliations

  1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, India

    P. Prakash

  2. Department of Computational Science and Humanities, Indian Institute of Information Technology Kottayam, Valavoor P.O, Kottayam, Pala, Kerala, 686635, India

    Reetha Thomas & T. Bakkyaraj

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  1. P. Prakash
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Prakash, P., Thomas, R. & Bakkyaraj, T. Invariant subspaces and exact solutions: \((1+1)\) and \((2+1)\)-dimensional generalized time-fractional thin-film equations. Comp. Appl. Math. 42, 97 (2023). https://doi.org/10.1007/s40314-023-02229-6

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