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Hilfer Fractional Differential Equations with Almost Sectorial Operators

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Abstract

In this article we consider an abstract Cauchy problem with the Hilfer fractional derivative and an almost sectorial operator. We introduce a suitable definition of a mild solution for this evolution equation and establish the existence result for a mild solution. We also give an example to highlight the applicability of theoretical results established.

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Acknowledgements

The authors are thankful to the anonymous referees for their valuable comments.

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Correspondence to Anjali Jaiswal.

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Jaiswal, A., Bahuguna, D. Hilfer Fractional Differential Equations with Almost Sectorial Operators. Differ Equ Dyn Syst (2020). https://doi.org/10.1007/s12591-020-00514-y

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Keywords

  • Almost sectorial operator
  • Cauchy problem
  • Hilfer fractional derivative
  • Measure of noncompactness