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Solvability of a fractional Cauchy problem based on modified fixed point results of non-compactness measures

  • Received: 02 April 2019 Accepted: 24 June 2019 Published: 19 July 2019
  • MSC : 34A08, 44A45, 47H10, 54H25

  • We study the solvability of a fractional Cauchy problem based on new development of fixed point theorem, where the operator is suggested to be non-compact on its domain. Moreover, we shall prove that the solution is bounded by a fractional entropy (entropy solution). For this purpose, we establish a collection of basic fixed point results, which generalizes and modifies some well known results. Our attention is toward the concept of a measure of non-compactness to generalize $\mu$-set contractive condition, using three control functions.

    Citation: Hemant Kumar Nashine, Rabha W. Ibrahim. Solvability of a fractional Cauchy problem based on modified fixed point results of non-compactness measures[J]. AIMS Mathematics, 2019, 4(3): 847-859. doi: 10.3934/math.2019.3.847

    Related Papers:

  • We study the solvability of a fractional Cauchy problem based on new development of fixed point theorem, where the operator is suggested to be non-compact on its domain. Moreover, we shall prove that the solution is bounded by a fractional entropy (entropy solution). For this purpose, we establish a collection of basic fixed point results, which generalizes and modifies some well known results. Our attention is toward the concept of a measure of non-compactness to generalize $\mu$-set contractive condition, using three control functions.


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