Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions

Abstract

In this research, we discuss the construction of analytic solution of homogenous initial boundary value problem including PDEs of fractional order. Since homogenous initial boundary value problem involves local fractional order derivative, it has classical initial and boundary conditions. By means of separation of variables method and the inner product defined on $L^2\left[0,l\right]$, the solution is constructed in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem including fractional derivative in local sense used in this study. Illustrative example presents the applicability and influence of separation of variables method on fractional mathematical problems.

Keywords

• Local Fractional Derivative
• Dirichlet boundary conditions
• Spectral method
• Separation of variables

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