EXISTENCE AND UNIQUENESS OF THE SOLUTION OF THE FRACTIONAL DIFFERENTIAL EQUATION VIA A NEW THREE STEPS ITERATION | ||||
| Journal of Fractional Calculus and Applications | ||||
| Volume 14, Issue 2, July 2023, Page 1-22 PDF (807.12 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/jfca.2023.209710.1018 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Haribhau Laxman Tidke  1; Gajanan S. Patil2
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| 1Department of Mathematics KBCNMU, Jalgaon | ||||
| 2Department of Mathematics KBCNMU, Jalgaon | ||||
| Abstract | ||||
| In this paper, we study the existence, uniqueness, and other qualitative properties of the solution of the differential equation with initial conditions of fractional order involving the Caputo fractional derivative. The tool employed in the analysis is based on the application of a new three steps iteration process introduced by V. Karakaya, Y. Atalan, K. Dogan, and NH. Bouzara [23] (i. e. V. Karakaya, Y. Atalan, K. Dogan and N. El Houda Bouzara, Some fixed point results for a new three steps iteration process in Banach spaces, Fixed Point Theory, 18, 2(2017), 625–640). The new three steps iteration method, due to simplicity and fastness, has attracted our attention and hence, it is used in this paper. Furthermore, the study of various properties such as dependence on initial given conditions, the closeness of solutions, and dependence on parameters and functions involved therein. The results obtained are illustrated through an example. The conclusion section is also included. | ||||
| Keywords | ||||
| New iterative method; Fractional derivative; Continuous dependence; Closeness; Parameters | ||||
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