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International Journal of Nonlinear Analysis and Applications، جلد ۱۴، شماره ۲، صفحات ۸۷-۱۰۰
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عنوان انگلیسی Existence of solution for a fractional differential equation via a new type of $(psi, F)$-contraction in $b$-metric spaces
چکیده انگلیسی مقاله 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.
کلیدواژه‌های انگلیسی مقاله Fixed point, $(alpha, beta)-S$-admissible mappings, Generalized $(psi, F)$-contraction, $b$-metric space, Differential equation
نویسندگان مقاله Francis Akutsah |
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

Akindele Adebayo Mebawondu |
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

Abass Hammed Anuoluwapo |
DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa

Kazeem Olalekan Aremu |
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

Narain Ojen Kumar |
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

نشانی اینترنتی https://ijnaa.semnan.ac.ir/article_7132_3bf531b51d39a63eabef8256ea4fda6d.pdf
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