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Positive solutions for generalized Caputo fractional differential equations with integral boundary conditions | ||
| Journal of Mathematical Modeling | ||
| مقاله 4، دوره 8، شماره 4، آذر 2020، صفحه 393-414 اصل مقاله (330.91 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2020.16125.1407 | ||
| نویسندگان | ||
| Hanan A. Wahash* 1؛ Satish K. Panchal1؛ Mohammed S. Abdo2 | ||
| 1Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India | ||
| 2Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen | ||
| چکیده | ||
| This article is devoted to the study of a new class of nonlinear fractional-order differential equations with integral boundary conditions involving a generalized version of the Caputo type fractional derivative with respect to another function $h$. In such a path, we transform the proposed problem into an equivalent integral equation. Then we build the upper and lower control functions of the nonlinear term without any monotone requirement except the continuity. By utilizing the method of upper and lower solutions, the fixed point theorems of Schauder and Banach, we obtain the existence and uniqueness of positive solutions for the problem at hand. Finally, we present some examples to illuminate our results. | ||
| کلیدواژه‌ها | ||
| Caputo fractional differential equation؛ integral boundary condition؛ existence of positive solution؛ control functions؛ fixed point theorem | ||
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آمار تعداد مشاهده مقاله: 1,105 تعداد دریافت فایل اصل مقاله: 1,217 |
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