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EN
In this research, we discuss the construction of the analytic solution of the homogenous initial boundary value problem including partial differential equations of fractional order. Since the homogenous initial boundary value problem involves a local fractional order derivative, it has classical initial and boundary conditions. By means of separation of the variables method and the inner product defined on L2 [0, l], the solution is constructed in the form of a Fourier series including the exponential function. The illustrative examples present the applicability and influence of the separation of variables method on time fractional diffusion problems. Moreover, as the fractional order α tends to 1, the solution of the fractional diffusion problem tends to the solution of the diffusion problem which proves the accuracy of the solution.
2  Solution of hybrid time fractional diffusion problem via weighted inner product
EN
In this research, we discuss the construction of the analytic solution of homogenous initial boundary value problem including partial differential equations of fractional order. Since the homogenous initial boundary value problem involves the Hybrid fractional order derivative with various coefficients functions, it has classical initial and boundary conditions. By means of separation of the variables method and the inner product defined on L 2 [0,l], the solution is constructed in the form of a Fourier series including the bivariate Mittag-Leffler function. An illustrative example presents the applicability and influence of the separation of variables method on time fractional diffusion problems. Moreover, as the fractional order α tends to 1, the solution of the fractional diffusion problem tends to the solution of the diffusion problem which proves the accuracy of the solution.
EN
The paper deals with the problem of boundary condition formulation for an electromagnetic field. The nonlinear boundary condition has been proposed. This condition has been introduced on the basis of Maxwell's equations. The nonlinear condition includes three well-known boundary conditions of Dirichlet, Neumann and Hankel. An example has been provided to show the usefulness of the boundary condition proposed. The fourth boundary condition enables us to reduce the region of numerical analysis.   Strona / 1    JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.