Fractional Differential Equations With Dependence on the Caputo–Katugampola Derivative
Copyright policy )Fractional Differential Equations With Dependence on the Caputo–Katugampola Derivative
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).
- Warsaw School of Economics Poland
- University of Aveiro Portugal
- Bialystok University of Technology Poland
- University of Aveiro Portugal
Fractional differential equations, Mathematics - Classical Analysis and ODEs, Caputo–Katugampola derivative, Fractional calculus, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Numerical methods
Fractional differential equations, Mathematics - Classical Analysis and ODEs, Caputo–Katugampola derivative, Fractional calculus, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Numerical methods
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