sh. rezapour

The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is effective and appropriate for obtaining the numerical solution of the timefractional Modified Camassa-Holm equation and Time fractional Modified Degasperis-Procesi equation.

Abstract. By using discrete fractional calculus, we investigate the existence of solutions for a self-adjoint nite Nabla fractional dierence equation on the time scale Nb a+1 via initial boundary conditions. Also, we check some conditions for uniqueness of solution of the problem. For nding the solution, we use the Green function which dened by using the Cauchy function. The principle of contraction mapping also plays an essential role in the existence of the solution. We provided two examples, a gure and numerical results to illustrate our main result. AMS Subject Classication: 34A12; 65L12. 

One of the considerable strategies for the investigation of integro-differential equation is stability. The notion of this strategy shows us that we can rest assured of the numerical results obtained from the computer software. Since there are usually large errors in the numerical results of singular differential equations, this strategy will help us to be able to examine singular equations more easily with computer software. In this work, we study the stability of a multisingular fractional boundary value problem in the sense of Hyers-Ulam stability.We also present three examples and three figures to illustrate our main result.