Local Fractional Fourier Series Solutions for Nonhomogeneous Heat Equations Arising in Fractal Heat Flow with Local Fractional Derivative

Fractional-Diffusion Solutions for Transient Local Temperature and Heat Flux

Applying properties of the Laplace transform, the transient heat diffusion equation can be transformed into a fractional (extraordinary) differential equation. This equation can then be modified, using the Fourier Law, into a unique expression relating the local value of the time-varying temperature (or heat flux) and the corresponding transient heat flux (or temperature). We demonstrate that t...

Fuzzy Local Fractional Differential Equations

Local Fractional Homotopy Perturbation Method for Solving Non-Homogeneous Heat Conduction Equations in Fractal Domains

In this article, the local fractional Homotopy perturbation method is utilized to solve the non-homogeneous heat conduction equations. The operator is considered in the sense of the local fractional differential operator. Comparative results between non-homogeneous and homogeneous heat conduction equations are presented. The obtained result shows the non-differentiable behavior of heat conducti...

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...

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...