Akutsah, Francis, Mebawondu, Akindele, Anuoluwapo, Abass, Aremu, Kazeem, Kumar, Narain. (1401). Existence of solution for a fractional differential equation via a new type of $(\psi, F)$-contraction in $b$-metric spaces. هنرهای کاربردی, 14(2), 87-100. doi: 10.22075/ijnaa.2022.23232.2500
Francis Akutsah; Akindele Adebayo Mebawondu; Abass Hammed Anuoluwapo; Kazeem Olalekan Aremu; Narain Ojen Kumar. "Existence of solution for a fractional differential equation via a new type of $(\psi, F)$-contraction in $b$-metric spaces". هنرهای کاربردی, 14, 2, 1401, 87-100. doi: 10.22075/ijnaa.2022.23232.2500
Akutsah, Francis, Mebawondu, Akindele, Anuoluwapo, Abass, Aremu, Kazeem, Kumar, Narain. (1401). 'Existence of solution for a fractional differential equation via a new type of $(\psi, F)$-contraction in $b$-metric spaces', هنرهای کاربردی, 14(2), pp. 87-100. doi: 10.22075/ijnaa.2022.23232.2500
Akutsah, Francis, Mebawondu, Akindele, Anuoluwapo, Abass, Aremu, Kazeem, Kumar, Narain. Existence of solution for a fractional differential equation via a new type of $(\psi, F)$-contraction in $b$-metric spaces. هنرهای کاربردی, 1401; 14(2): 87-100. doi: 10.22075/ijnaa.2022.23232.2500

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
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
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