A Priori Estimates for the Solution of an Initial Boundary Value Problem of Fluid Flow through Fractured Porous Media

The paper studies a model of fluid flow in fractured porous medium which fractures are distributed uniformly over the volume. This includes nonlinear equation containing several terms with fractional derivatives sense Caputo order belonging to interval 1,2. relevance studying this problem is determined by its practical significance oil industry, since most world’s reserves these types reservoirs. uniqueness solution differential form and dependence on initial data right-hand side proved. A numerical method proposed based use finite difference approximation for integer time element spatial direction. change variables introduced reduce derivatives. Furthermore, derivative approximated using L1-method. stability convergence rigorously theoretical confirmed results tests media known exact solution.