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https://ptsldigital.ukm.my/jspui/handle/123456789/500451| Title: | On the modified caputo's derivative operator |
| Authors: | Jamal Yousef Mohammad Salah (P43526) |
| Supervisor: | Maslina Darus, Prof. Dr. |
| Keywords: | Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia Fractional calculus Univalent functions Differential equations |
| Issue Date: | Apr-2013 |
| Description: | The main subject of this work coincides with the recently adapted methodology in thetheory of univalent functions via applications of fractional calculus. The Caputo's definition of fractional derivative of orderαhas not been obviously applied in thefield. However, it plays a vital role in other areas like physics and engineering dueto its simple restrictions compared to Liouville's integral operator. By modifyingthe Caputo's derivative operator, a new modified Caputo's operator is defined in thisthesis. Consequently, new subclasses of analytic functions are introduced, and basicproperties, such as distortion theorems, extremal functions, coefficient bounds, theintegral transform, superordination and subordination results are discussed. The radiiof basic well known properties (univalency, starlikeness, convexity) are also obtainedfor the new subclasses. Moreover, some results of the modified Hadamard product(convolution) are provided by applying the famous Cauchy-Shwartz inequality. Inorder to expand the application of the modified Caputo's operator, two new subclassesof analyticp-valent functions are introduced and investigated through the concepts ofneighbourhood and inclusion relations. Further, the definition of univalency with respectto 1 together with subordination are used to solve a sharp functional of Fekete-Szeg ̈oproblem. Moreover, some interesting results related to Hankel determinant are obtained,Certification of Master's / Doctoral Thesis" is not available |
| Pages: | 96 |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
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|---|---|---|---|---|
| ukmvital_120147+SOURCE1+SOURCE1.0.PDF Restricted Access | 772.75 kB | Adobe PDF |  View/Open |
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