Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order | Zendy

Ming Li | Zendy; Wei Zhao | Zendy

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Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order

Author(s) -

Ming Li,

Wei Zhao

Publication year - 2013

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2013/806984

Subject(s) - mathematics , type (biology) , fractional calculus , operator (biology) , integral equation , summation equation , mathematical analysis , order (exchange) , operational calculus , inverse , daniell integral , calculus (dental) , fourier integral operator , medicine , ecology , biochemistry , chemistry , geometry , dentistry , finance , repressor , gene , transcription factor , economics , biology

This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type

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