Logarithmic transformation between (variable-order) Caputo and Caputo-Hadamard fractional problems and applications

Abstract We present a logarithmic transformation reducing the (variable-order) Caputo–Hadamard fractional problems to their Caputo analogues. Then the analysis of the former may be directly obtained from the existing results for the latter by the inverse transformation. By employing this transformation method, we connect these two kinds of problems and obtain new analysis results for variable-order Caputo–Hadamard fractional operators and models.

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