Hadamard-type fractional calculus in Banach spaces

Original Paper


In this pages, we present the definitions and some properties of the Hadamard-type fractional Pettis integrals (and corresponding fractional derivatives) for the functions that take values in Banach space. Further, we show that a well known properties of the Hadamard-type fractional calculus over the space of real-valued functions also hold in Banach spaces. Some emphasizes examples are demonstrated. Meanwhile, we construct an example of a function that has no pseudo derivative everywhere, but has a Hadamard-type fractional derivative. As far as we know, the topic of this paper was never investigated before, and so is new.


Fractional calculus Pettis integrals 

2000 Mathematics Subject Classification

26A33 34G20 



I would like to express my gratitude to Prof. Martin Väth, for his advise, guidance, patience and continuous support.


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© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Faculty of SciencesAlexandria UniversityAlexandriaEgypt

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