Applications of New Time and Spatial Fractional Derivatives with Exponential Kernels

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New numerical approach for fractional differential equations (2017, background): “A lot has been reported in the literature on various fractional derivatives, ranging from the Riemann-Liouville to AtanganaBaleanu fractional derivative versions [3, 5, 6].”
Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems (2016, methodology): “Recently, FDs involving the kernels of the exponential and Mittag-Leffler functions were reported in [17,18,19,20,21,22,23,24].”
New aspects of time fractional optimal control problems within operators with nonsingular kernel (2020, background): “One of the newly defined operators is Caputo-Fabrizio (CF) fractional derivative, which is capable of eliminating singular kernel in the definition of classical Caputo derivative [18].”
Transient heat diffusion with a non-singular fading memory: From the Cattaneo constitutive equation with Jeffrey’s Kernel to the Caputo-Fabrizio time-fractional derivative (2016, background): “Caputo and Fabrizio it was assumed for convenience that M(α) = 1 that leads to the final definition of the new time-fractional derivative [1, 3, 4] in the form of eq.”
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model (2016, background): “However this issue was, so far, independently solved in [5] and [6], respectively.”