Progress in Fractional Differentiation & Applications

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This paper deals with the application of a novel variable-order and constant-order fractional derivatives in the Newton’s law of cooling. The variable-order fractional derivative can be set as a smooth function, bounded on (0,1], while the constant-order fractional derivative can be set as a fractional equation, bounded on (0,1]. We solved analytically the fractional equations using the Laplace transform. Numerical simulations were performed for different values of fractional order. The integer-order classical model is recovered when the order of the fractional derivative is equal to 1. Based upon the results obtained, the efficiency rates of the fractional-order operators with non-singular kernel are higher than that of the existing fractional model with singular kernel.

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