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| Title: | A Short Note on the Quasilinearization Method for Fractional Differential Equations |
| Authors: | Vijesh, Antony |
| Keywords: | Differential equations;Newton-Raphson method;Riccati equations;Existence and uniqueness;Fractional derivatives;Fractional differential equations;Fractional order;Monotone iterative techniques;Newton's methods;Quasi-linearization;Quasi-linearization methods;Iterative methods |
| Issue Date: | 2016 |
| Publisher: | Taylor and Francis Inc. |
| Citation: | Vijesh, V. A. (2016). A short note on the quasilinearization method for fractional differential equations. Numerical Functional Analysis and Optimization, 37(9), 1158-1167. doi:10.1080/01630563.2016.1188827 |
| Abstract: | Recent literature shows that for certain classes of fractional differential equations the monotone iterative technique fails to guarantee the quadratic convergence of the quasilinearization method. The present work proves the quadratic convergence of the quasilinearization method and the existence and uniqueness of the solution of such a class of fractional differential equations. Our analysis depends upon the classical Kantorovich theorem on Newton's method. Various examples are discussed in order to illustrate our approach. © 2016, Copyright © Taylor & Francis Group, LLC. |
| URI: | https://doi.org/10.1080/01630563.2016.1188827 https://dspace.iiti.ac.in/handle/123456789/6680 |
| ISSN: | 0163-0563 |
| Type of Material: | Journal Article |
| Appears in Collections: | Department of Mathematics |
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