Third-order differential subordination and superordination involving a fractional operator

Rabha W. Ibrahim; Muhammad Zaini Ahmad; Hiba F. Al-Janaby

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

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The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.

How to cite

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Rabha W. Ibrahim, Muhammad Zaini Ahmad, and Hiba F. Al-Janaby. "Third-order differential subordination and superordination involving a fractional operator." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/275994>.

@article{RabhaW2015,
abstract = {The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.},
author = {Rabha W. Ibrahim, Muhammad Zaini Ahmad, Hiba F. Al-Janaby},
journal = {Open Mathematics},
keywords = {Fractional calculus; Fractional integral operator; Subordination; Superordination; Unit disk; Analytic function},
language = {eng},
number = {1},
pages = {null},
title = {Third-order differential subordination and superordination involving a fractional operator},
url = {http://eudml.org/doc/275994},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Rabha W. Ibrahim
AU - Muhammad Zaini Ahmad
AU - Hiba F. Al-Janaby
TI - Third-order differential subordination and superordination involving a fractional operator
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.
LA - eng
KW - Fractional calculus; Fractional integral operator; Subordination; Superordination; Unit disk; Analytic function
UR - http://eudml.org/doc/275994
ER -

References

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