Conservation laws of (3+α)-dimensional time-fractional diffusion equation

The concept of Lie–Backlund symmetry plays a fundamental role in applied mathematics. It is clear that in order to find conservation laws for a given partial differential equations (PDEs) or fractional differential equations (FDEs) by using Lagrangian function, firstly, we need to obtain the symmetries of the considered equation. Fractional derivation is an efficient tool for interpretation of mathematical methods. Many applications of fractional calculus can be found in various fields of sciences as physics (classic, quantum mechanics and thermodynamics), biology, economics, engineering and etc. So in this paper, we present some effective application of fractional derivatives such as fractional symmetries and fractional conservation laws by fractional calculations. In the sequel, we obtain our results in order to find conservation laws of the time-fractional equation in some special cases.