Local Fractional Fourier Series Method for Solving Nonlinear Equations with Local Fractional Operators

Exact Solution for Nonlinear Local Fractional Partial Differential Equations

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...

Fuzzy Local Fractional Differential Equations

On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators

Hossein Jafari 1,2,*, Hassan Kamil Jassim 2,3, Fairouz Tchier 4 and Dumitru Baleanu 5,6 1 Department of Mathematical Sciences, University of South Africa (UNISA), Pretoria 0003, South Africa 2 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar 47416, Iran; [email protected] 3 Department of Mathematics, Faculty of Education for Pure Sciences, U...

The analytical solutions for Volterra integro-differential equations within Local fractional operators by Yang-Laplace transform

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

Solving nonlinear space-time fractional differential equations via ansatz method

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...