A NEW MESHLESS METHOD BASED ON THERADIAL BASIS FUNCTIONS FOR SOLVING THEFRACTIONAL DIFFERENTIAL EQUATIONS

In the current paper a new and very e cient meshfreetechnique based on the radial basis functions is introduced whichcould be used for solving general fractional di erential equationwith high accuracy. In this paper, Gaussian function is selected asbasis function in the process and then an explicit formulation ispresented to provide a fractional derivative of the caputo type forthis radial basis function. Then a collocation radial basis functionmethod is employed directly to approximate the numerical solutionof fractional di erential equations. Illustrative example is includedto demonstrate the validity and applicability of the presented tech-nique