Abstract
AbstractIn this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the time fractional Hunter–Saxton equation, a time fractional nonlinear diffusion equation, a time fractional thin-film equation, the fractional Whitman–Broer–Kaup-type equation, and a system of time fractional diffusion equations.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference23 articles.
1. Diethelm, K.: The Analysis of Fractional Differential Equations, an Application-Oriented Exposition Using Differential Operators of Caputo Type. Springer, Berlin (2010)
2. Kilbas, A., Srivastava, H., Trujillo, J.: Theory and Applications of Fractional Differential Equations. North-Holland, New York (2006)
3. Wu, G.C., Baleanu, D.: Variational iteration method for the Burgers’ flow with fractional derivatives—new Lagrange multipliers. Appl. Math. Model. 37(9), 6183–6190 (2013)
4. Sun, H., Zhang, Y., Baleanu, D., Chen, W., Chen, Y.: A new collection of real world applications of fractional calculus in science and engineering. Commun. Nonlinear Sci. Numer. Simul. 64, 213–231 (2018)
5. Elsaid, A., Abdel Latif, M.S., Maneea, M.: Similarity solutions of fractional order heat equations with variable coefficients. Miskolc Math. Notes 17(1), 245–254 (2016)
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