On more general forms of proportional fractional operators-Reference-Cited by-同舟云学术

On more general forms of proportional fractional operators

Published:2020-01-01 Issue:1 Volume:18 Page:167-176
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Jarad Fahd¹,Alqudah Manar A.²,Abdeljawad Thabet³⁴⁵

Affiliation:

1. Department of Mathematics , Çankaya University , 06790 , Ankara , Turkey

2. Department of Mathematical Sciences , Princess Nourah Bint Abdulrahman University , P.O. Box 84428 , Riyadh , 11671 , Saudi Arabia

3. Department of Mathematics and General Sciences , Prince Sultan University , P. O. Box 66833, 11586 , Riyadh , Saudi Arabia

4. Department of Medical Research , China Medical University , 40402 , Taichung , Taiwan

5. Department of Computer Science and Information Engineering , Asia University , Taichung , Taiwan

Abstract

Abstract In this article, more general types of fractional proportional integrals and derivatives are proposed. Some properties of these operators are discussed.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0014/pdf

Reference35 articles.

1. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego CA, 1999.

2. S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, 1993.

3. R. Hilfer, Applications of Fractional Calculus in Physics, Word Scientific, Singapore, 2000.

4. L. Debnath, Recent applications of fractional calculus to science and engineering, Int. J. Math. Math. Sci. 2003 (2003), no. 54, 3413–3442.

5. A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Application of Fractional Differential Equations, Elsevier, Amsterdam, 2006.

Cited by 73 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. New Grüss’s inequalities estimates considering the φ-fractional integrals;Partial Differential Equations in Applied Mathematics;2024-09

2. Existence and Stability of Solutions for p-Proportional ω-Weighted κ-Hilfer Fractional Differential Inclusions in the Presence of Non-Instantaneous Impulses in Banach Spaces;Fractal and Fractional;2024-08-14

3. On generalized $(k,\psi )$-Hilfer proportional fractional operator and its applications to the higher-order Cauchy problem;Boundary Value Problems;2024-07-03

4. Fractional proportional linear control systems: A geometric perspective on controllability and observability;Constructive Mathematical Analysis;2024-06-15

5. Ulam type stability analysis for generalized proportional fractional differential equations;Carpathian Mathematical Publications;2024-05-24