In this paper, we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy-type problem, with dependence on the Caputo–Katugampola derivative, is proved. A decomposition formula for the Caputo–Katugampola derivative is obtained. This formula allows us to provide a simple numerical procedure to solve the fractional differential equation (FDE).
Fractional Differential Equations With Dependence on the Caputo–Katugampola Derivative
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 12, 2015; final manuscript received July 29, 2016; published online September 16, 2016. Assoc. Editor: Brian Feeny.
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Almeida, R., Malinowska, A. B., and Odzijewicz, T. (September 16, 2016). "Fractional Differential Equations With Dependence on the Caputo–Katugampola Derivative." ASME. J. Comput. Nonlinear Dynam. November 2016; 11(6): 061017. https://doi.org/10.1115/1.4034432
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