ON AN INITIAL AND FINAL VALUE PROBLEM FOR FRACTIONAL NONCLASSICAL DIFFUSION EQUATIONS OF KIRCHHOFF TYPE

We study for nonlinear Kirchhoff's model of pseudo parabolic type by considering its two different problems. center dot For initial value problem, we obtain the results on the existence and regularity of solutions. Moreover, we also prove that the solutions u corresponding with beta < 1 of the problem convergence to u for beta = 1. center dot For final value problem, we show that the ill-posed property in the sense of Hadamard is occurring. Using the Fourier truncation method to regularize the problem. We establish some stability estimates in the H1 and LP norms under some a-priori conditions on the sought solution.