Lie symmetry analysis for fractional evolution equation with $\psi$-Riemann-Liouville derivative

Junior C. A. Soares; Felix S. Costa; J. Vanterler C. Sousa; Maria V. S. Sousa; Amália R. E. Pereira

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arXiv · 2401.08601

Lie symmetry analysis for fractional evolution equation with $\psi$-Riemann-Liouville derivative

Junior C. A. Soares·Felix S. Costa·J. Vanterler C. Sousa·Maria V. S. Sousa·Amália R. E. Pereira

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Abstract

We present the applycation of theory of Lie group analysis with $\psi$-Riemann-Liouville fractional derivative detailing the construction of infinitesimal prolongation to obtain Lie symmetries. In additional, is addressed the invariance condition without the need to impose that the lower limit of fractional integral is fixed. We find an expression that expands the knowledge regarding the study of exact solutions for fractional differential equations. We use of the framework developed in \cite{zaky2022note} to present our understanding of the extension of $\psi$-Riemann-Liouville fractional derivative. It is demonstrate the Leibniz type rule for the derivative operator in question for built the prolongation. At last, we calculate the Lie symmetries of the generalized Burgers equation and fractional porous medium equation.

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Junior C. A. Soares, Felix S. Costa, J. Vanterler C. Sousa, Maria V. S. Sousa, Amália R. E. Pereira. 2023-11-20. Lie symmetry analysis for fractional evolution equation with $\psi$-Riemann-Liouville derivative. https://arxiv.org/abs/2401.08601

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