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Keywords = srivastava-owa fractional operators

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17 pages, 2931 KB  
Article
New Results on (r,k,μ)-Riemann–Liouville Fractional Operators in Complex Domain with Applications
by Adel Salim Tayyah and Waggas Galib Atshan
Fractal Fract. 2024, 8(3), 165; https://doi.org/10.3390/fractalfract8030165 - 13 Mar 2024
Cited by 16 | Viewed by 1818
Abstract
This paper introduces fractional operators in the complex domain as generalizations for the Srivastava–Owa operators. Some properties for the above operators are also provided. We discuss the convexity and starlikeness of the generalized Libera integral operator. A condition for the convexity and starlikeness [...] Read more.
This paper introduces fractional operators in the complex domain as generalizations for the Srivastava–Owa operators. Some properties for the above operators are also provided. We discuss the convexity and starlikeness of the generalized Libera integral operator. A condition for the convexity and starlikeness of the solutions of fractional differential equations is provided. Finally, a fractional differential equation is converted into an ordinary differential equation by wave transformation; illustrative examples are provided to clarify the solution within the complex domain. Full article
(This article belongs to the Section General Mathematics, Analysis)
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9 pages, 209 KB  
Article
On a New Solution of Fractional Differential Equation Using Complex Transform in the Unit Disk
by Rabha W. Ibrahim and Maslina Darus
Math. Comput. Appl. 2014, 19(2), 152-160; https://doi.org/10.3390/mca19020152 - 1 Aug 2014
Cited by 7 | Viewed by 1454
Abstract
The Möbius transform of fractional differential equation (Riccati type) is employed to construct new exact solutions for some nonlinear fractional differential equations. The fractional operators are taken in sense of the modified Srivastava-Owa fractal in the unit disk. Examples are illustrated for problems [...] Read more.
The Möbius transform of fractional differential equation (Riccati type) is employed to construct new exact solutions for some nonlinear fractional differential equations. The fractional operators are taken in sense of the modified Srivastava-Owa fractal in the unit disk. Examples are illustrated for problems in biology, economic and physics. Full article
9 pages, 320 KB  
Article
A Note on Fractional Differential Subordination Based on the Srivastava-Owa Fractional Operator
by Rabha W. Ibrahim and Maslina Darus
Math. Comput. Appl. 2014, 19(2), 115-123; https://doi.org/10.3390/mca19020115 - 1 Aug 2014
Cited by 2 | Viewed by 1433
Abstract
In this work, we consider a definition for the concept of fractional differential subordination in sense of Srivastava-Owa fractional operators. By employing some types of admissible functions involving differential operator of fractional order, we illustrate applications. Full article
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