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Integral transforms of the Hilfer-type fractional derivatives
  • Felix Costa,
  • Junior Cesar Alves Soares,
  • Stefânia Jarosz
Felix Costa

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Junior Cesar Alves Soares
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Stefânia Jarosz
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In this paper, some important properties concerning the Hilfer-type fractional derivatives are discussed. Integral transforms for these operators are derived as particular cases of the Jafari transform. These integral transforms are used to derive a fractional version of the fundamental theorem of calculus.

Keywords: Integral transforms, Jafari transform, \(\kappa\)-gamma function, \(\kappa\)-beta function, \(\kappa\)-Hilfer fractional derivative, \(\kappa\)-Riesz fractional derivative, \(\kappa\)-fractional operators, \((\kappa,\rho)\)-Hilfer fractional derivative.