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Impulsive initial value problems for a class of implicit fractional differential equations | ||
| Computational Methods for Differential Equations | ||
| مقاله 10، دوره 8، شماره 1، فروردین 2020، صفحه 141-154 اصل مقاله (394.89 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2019.9455 | ||
| نویسندگان | ||
| Amjad S. Shaikh* 1؛ Bhausaheb R. Sontakke2 | ||
| 1Department of Mathematics, AKI's Poona College of Arts, Science and Commerce, Camp, Pune, India | ||
| 2Department of Mathematics, Pratishthan Mahavidyalaya, Paithan, Dist. Aurangabad, India | ||
| چکیده | ||
| In this article we consider, impulsive initial value problems for a class of implicit fractional differential equations involving the Caputo fractional derivative of order β in (1,2]. The solutions of this nonlinear equation are analyzed by establishing sufficient conditions for existence and uniqueness using Banach's contraction mapping principle and the Schaefer's fixed point theorem. In addition, using the Banach contraction principle, we establish uniqueness result. To demonstrate main results two examples are presented. | ||
| کلیدواژهها | ||
| Initial value problem؛ Implicit fractional differential equations؛ Impulses؛ Fixed point theorem | ||
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