In this paper we find the exact solution of Burger's equation after reducing it to Bernoulli equation. We compare this solution with that given by Kaya where he used Adomian decomposition method, the solution given by chakrone where he used the Variation iteration method (VIM)and the solution given by Eq(5)in the paper of M. Javidi. We notice that our solution is better than their solutions.

حصلنا من بحثنا هذا على الحل المضبوط (Exact) لمعادلة بيركر بعد تحويلها إلى معادلة برنو لي وتمت مقارنة هذا الحل مع حل "Kaya"الذي استخدم طريقة تجزئة ادومين وحل "Chakrone" الذي أستخدم طريقة التغاير المتكرر وحل "Javidi" المعطى بالعلاقة (5)وتبين ان حلنا هذا افضل من حلولهم للبساطه الصيغة

Burger's equation --- kdv equation --- PDF.

In this article, a Legendre wavelet- Chebyshev wavelet spectral collocation method is proposed for solving fractional order space-time Burger's equation with the Legendre wavelet and Chebyshev wavelet operational matrices of fractional derivatives. The fractional derivative is described in the Caputo sense. The proposed method is based on Legendre wavelet-Chebyshev wavelet for space and time variables respectively. This method will reduc the problem under consideration to the solution of nonlinear algebraic equations. In order to confirm the efficiency of the proposed method, two numerical examples are implemented and comparing the numerical solution with the exact one, as well as, of other methods in given literatures, we demonstrate the high accuracy and efficiency of the proposed method.

Fractional Burger's equation --- Legendre wavelet-Chebyshev wavelet --- spectral collocation method