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A certain coupled system of $q$-FDEs on two consecutive intervals under Dirichlet conditions via Krasnoselskii's theorem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 05 مهر 1404 اصل مقاله (534.77 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.34514.5154 | ||
| نویسندگان | ||
| Mohammad Esmael Samei* 1؛ Mohammad Izadi2؛ Mohammed K. A. Kaabar3 | ||
| 1Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran | ||
| 2Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman 76169-14111, Iran | ||
| 3Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia | ||
| تاریخ دریافت: 01 تیر 1403، تاریخ پذیرش: 24 بهمن 1403 | ||
| چکیده | ||
| In this study, we use certain mathematical tools to analyze the solutions of a system of fractional $q$-differential equation ${}^C\mathbb{D}_{q}^{\sigma_i} [\wp](\mathfrak{t}) = \mathfrak{w}_i( \mathfrak{t}, \wp(\mathfrak{t}), {}^C\mathbb{D}_{q}^{{}_i\nu_{j}} [\wp](\mathfrak{t}), \mathbb{I}_{q}^{{}_{i}\nu_j} [\wp] (\mathfrak{t}) )$, $i=~1$ whenever $\mathfrak{t} \in [0, \mathfrak{t}_0]$, and $i=2$ whenever $\mathfrak{t} \in [\mathfrak{t}_0, 1]$, for $j=1,2$, such as fixed point theorem of Krasnoselskii and Banach contraction principle, under simultaneous Dirichlet boundary conditions. Here, we use standard definitions of the Liouville-Caputo fractional type $q-$derivative and Riemann-Liouville $q-$integral. Some illustrative examples with numerical results are discussed, too. | ||
| کلیدواژهها | ||
| nonlinear fractional equation؛ fractional $q-$differential equation؛ Dirichlet boundary conditions؛ Riemann--Liouville $q-$integral | ||
| مراجع | ||
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