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A Fractional Calculus Approach to Study Newton’s Law of Cooling |
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PP: 275-287 |
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doi:10.18576/pfda/080207
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Author(s) |
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Nikita Bhangale,
Krunal B. Kachhia,
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Abstract |
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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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