fractional calculus

This study proposes a novel numerical approach for addressing both linear and nonlinear initial fractional order differential equations (FDEs) through the implementation of the Jacobi–Gauss–Radau (JGR) integrated with Caputo fractional derivatives.  The problem is effectively transformed into a simplified system of FDEs, encompassing the unknown coefficients, by employing shifted JGR points for the FDEs and their initial conditions.  For the purpose of investigating the effectiveness and accuracy of the introduced method, some numerical illustrations are provided for various linear and nonl

Image inpainting is an important research area in image processing.  Its main purpose is to supplement missing or damaged domains of images using information from surrounding areas.  This step can be performed by using nonlinear diffusive filters requiring a resolution of partial differential evolution equations.  In this paper, we propose a filter defined by a partial differential nonlinear evolution equation with spatial fractional derivatives.  Due to this, we were able to improve the performance obtained by known inpainting models based on partial differential equations and extend certa