Some properties of pseudo-fractional operators

  • Azizollah Babakhani
  • Milad Yadollahzadeh
  • Abdolali Neamaty


In the present paper, we discuss the pseudo-fractional calculus, including two fields of fractional calculus and pseudo-analysis. We also provide pseudo-fractional integral/derivative operators on a semiring \(([a,b],\oplus ,\odot )\). Then, some basic properties of these operators are proposed such as the Leibniz rule, chain rule and g-Laplace transform formulas.


Pseudo-multiplication Pseudo-addition Semiring Pseudo-fractional integrals Pseudo-fractional derivatives The Leibniz rule Pseudo-Laplace transform 

Mathematics Subject Classification

47GXX 26A33 47AXX 



The authors would like to thank to the anonymous referees for their valuable comments and suggestions.


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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • Azizollah Babakhani
    • 1
  • Milad Yadollahzadeh
    • 2
  • Abdolali Neamaty
    • 2
  1. 1.Department of MathematicsBabol Noshirvani University of TechnologyBabolIran
  2. 2.Department of Mathematics, Faculty of mathematical SciencesUniversity of MazandaranBabolsarIran

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