We investigated analytical solutions for the nonlinear differential-difference equations (DDEs) having fractional-order derivative. We employed the discrete tanh method in computations. Performance of trigonometric functions, dark one solitons and rational solutions are discussed in detail. The results with reliable parameters are illustrated via 2-D and 3-D graphs.
In this paper, we study an inverse problem for an inhomogeneous time-fractional diffusion equation in the one-dimensional real-positive semiaxis domain. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative. After we show that the inverse problem is severely ill posed, we apply a modified regularization method based on the solution in the frequency domain to solve the inverse problem. A convergence estimate is also derived. We present two numerical examples to show the efficiency of the method.
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