Abstract
Abstract The idea of functions of bounded differential variation was introduced by Bhatt, Dabhi and Kachhia in [2]. In the present paper, we introduce functions of bounded fractional differential variation using the Caputo-type fractional derivative instead of the commonly used first-order derivative. Various properties and relation with some known results of classical analysis are also studied. We prove that the space BFDV [ a , b ] ${\mathrm{BFDV}[a,b]}$ of all functions of bounded fractional differential variation on [ a , b ] ${[a,b]}$ is a normed algebra under certain type of norms.
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