Nikan, O.Avazzadeh, Z.Machado, J. A. Tenreiro2021-09-292021http://hdl.handle.net/10400.22/18627The generalized Cattaneo model describes the heat conduction system in the perspective of time-nonlocality. This paper proposes an accurate and robust meshless technique for approximating the solution of the time fractional Cattaneo model applied to the heat flow in a porous medium. The fractional derivative is formulated in the Caputo sense with order 1<α<2 . First, a finite difference technique of convergence order O(δt3−α) is adopted to achieve the temporal discretization. The unconditional stability of the method and its convergence are analysed using the discrete energy technique. Then, a local meshless method based on the radial basis function partition of unity collocation is employed to obtain a full discrete algorithm. The matrices produced using this localized scheme are sparse and, therefore, they are not subject to ill-conditioning and do not pose a large computational burden. Two examples illustrate in computational terms of the accuracy and effectiveness of the proposed method.engCaputo fractional derivativeFractional Cattaneo equationRBF-PUFinite differenceStabilityConvergencejournal article10.1016/j.apm.2021.07.025