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Existence of solution for a fractional differential equation via a new type of $(\psi, F)$-contraction in $b$-metric spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 7، دوره 14، شماره 2، اردیبهشت 2023، صفحه 87-100 اصل مقاله (444.5 K) | ||
| نوع مقاله: Special issue editorial | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.23232.2500 | ||
| نویسندگان | ||
| Francis Akutsah1؛ Akindele Adebayo Mebawondu* 1، 2؛ Abass Hammed Anuoluwapo2؛ Kazeem Olalekan Aremu1؛ Narain Ojen Kumar1 | ||
| 1School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa | ||
| 2DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa | ||
| تاریخ دریافت: 03 اردیبهشت 1400، تاریخ بازنگری: 24 تیر 1401، تاریخ پذیرش: 13 آبان 1401 | ||
| چکیده | ||
| In this paper, we further develop the notion of cyclic $(\alpha, \beta)$-admissible mappings introduced in (\cite{tac}, S. Chandok, K. Tas, A. H. Ansari, \emph{Some fixed point results for TAC-type contractive mappings,} J. Function spaces, 2016, Article ID 1907676, 1--6) and $(\psi, F)$-contraction mappings introduced in ( \cite{wad1}, D. Wardowski, \emph{Solving existence problems via $F$-contractions,} Proceedings of the American Mathematical Society, 146 (4), (2018), 1585--1598), in the framework of $b$-metric spaces. To achieve this, we introduce the notion of $(\alpha,\beta)-S$-admissible mappings and a new class of generalized $(\psi, F)$-contraction types and establish a common fixed point and fixed point results for these classes of mappings in the framework of complete $b$-metric spaces. As an application, we establish the existence and uniqueness of the solutions to differential equations in the framework of fractional derivatives involving Mittag-Leffler kernels via the fixed point technique. The results obtained in this work provide extension as well as substantial generalization and improvement of the fixed point results obtained in \cite{tac,wad1, wad} and several well-known results on fixed point theory and its applications. | ||
| کلیدواژه‌ها | ||
| Fixed point؛ $(\alpha؛ \beta)-S$-admissible mappings؛ Generalized $(\psi؛ F)$-contraction؛ $b$-metric space؛ Differential equation | ||
| مراجع | ||
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