A general method of fractional dynamics, i.e., fractional Jacobi last multiplier method, and its applications

Solution of the fractional diffusion equation by using Caputo-Fabrizio derivative: application to intrinsic arsenic diffusion in germanium

“…In recent decades, researchers have paid great attention to fractional calculus and its applications. It has been used successfully for modelling many phenomena in different areas of sciences and engineering as quantum physics, continuum mechanics, viscoelastic and viscoplastic flow, electrical circuits, control theory, image processing, viscoelasticity, biology and hydrodynamics (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13]). Historically, the emergence of this type of calculus was at the end of the seventeenth century, when Gottfried Leibniz sent a letter to L'Hospital which he raised a question about the possibility of the meaning of derivatives with integer order in which be generalized to derivatives with non-integer orders [14].…”