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The task:

$$ \frac{\partial^\gamma}{\partial t^\gamma}u(x, t) = D(x)\left( \frac{(1+\beta)}{2}\frac{\partial _+^\alpha}{\partial x^\alpha} + \frac{(1-\beta)}{2}\frac{\partial _-^\alpha}{\partial x^\alpha} \right)u(x, t) + V(x)\frac{\partial}{\partial x}u(x, t) + f(x, t) $$

$$ u(x, 0) = \psi(x) $$

$$ u(L, t) = \phi_L(t) $$

$$ u(R, t) = \phi_R(t) $$

$$ \alpha \in (1; 2); \gamma \in (0; 1); \beta \in [-1; 1] $$