This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral, which actually does not exist. Besides, our results also cover some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.
On Finite Part Integrals and Hadamard-Type Fractional Derivatives
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 18, 2017; final manuscript received August 29, 2017; published online July 26, 2018. Assoc. Editor: Dumitru Baleanu.
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Ma, L., and Li, C. (July 26, 2018). "On Finite Part Integrals and Hadamard-Type Fractional Derivatives." ASME. J. Comput. Nonlinear Dynam. September 2018; 13(9): 090905. https://doi.org/10.1115/1.4037930
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