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Approximation of functions by Complex conformable derivative bases in Frechet spaces
  • Gamal HAssan,
  • Emad Abdel-salam,
  • Rashwan Rashwan
Gamal HAssan
Assiut University Faculty of Science

Corresponding Author:[email protected]

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Emad Abdel-salam
Department of Mathematics, Faculty of Science, Assiut University, New Valley Branch, El-Kharja 72511, Egypt
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Rashwan Rashwan
Assiut University Faculty of Science
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In the present paper the representation, in different domains, of analytic functions by complex conformable fractional derivative bases (CCFDB) and complex conformable fractional integral bases (CCFIB) in Frechet space are investigated . Theorems are proved to show that such representation is possible in closed disks, open disks, open regions surrounding closed disks, at the origin and for all entire functions. Also, some results concerning the growth order and type of CCFDB and CCFIB are determined. Moreover the T-property of CCFDB and CCFIB are dis- cussed. The obtained results recover some known results when alpha = 1. Finally, some applications to the CCFDB and CCFIB of Bernoulli, Euler, Bessel and Chebyshev polynomials have been studied.
09 Sep 2021Submitted to Mathematical Methods in the Applied Sciences
10 Sep 2021Submission Checks Completed
10 Sep 2021Assigned to Editor
24 Sep 2021Reviewer(s) Assigned
23 Dec 2021Review(s) Completed, Editorial Evaluation Pending
08 Mar 2022Editorial Decision: Revise Minor
13 Jun 20221st Revision Received
14 Jun 2022Assigned to Editor
14 Jun 2022Submission Checks Completed
14 Jun 2022Reviewer(s) Assigned
21 Jun 2022Review(s) Completed, Editorial Evaluation Pending
22 Jun 2022Editorial Decision: Revise Minor
04 Jul 20222nd Revision Received
05 Jul 2022Submission Checks Completed
05 Jul 2022Assigned to Editor
11 Jul 2022Reviewer(s) Assigned
19 Jul 2022Review(s) Completed, Editorial Evaluation Pending
27 Jul 2022Editorial Decision: Accept