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Fractal calculus involving gauge function

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2016

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Elsevier Science Bv

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Abstract

Henstock-Kurzweil integral or gauge integral is the generalization of the Riemann integral. The functions which are not integrable because of singularity in the senses of Lebesgue or Riemann are gauge integrable. In this manuscript, we have generalized F-alpha-calculus using the gauge integral method for the integrating of the functions on fractal set subset of real-line where they have singularities. The suggested new method leads to the wider class of functions on the fractal subset of real-line that are *F-alpha-integrable, Using gauge function we define *F-alpha-derivative of functions their *F-alpha-derivative is not exist. The reported results can be used for generalizing the fundamental theorem of F-alpha-calculus

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Fractal Calculus, Fractional Derivative, Gauge Integral, Fractal Dimension

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Citation

Golmankhaneh,A.K., Baleanu, D. (2016). Fractal calculus involving gauge function. Communications In Nonlinear Science And Numerical Simulation, 37, 125-130. http://dx.doi.org/10.1016/j.cnsns.2016.01.007

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Communications In Nonlinear Science And Numerical Simulation

Volume

37

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Start Page

125

End Page

130