SOME FIXED POINT RESULTS WITH APPLICATION TO FRACTIONAL DIFFERENTIAL EQUATION VIA NEW TYPE OF DISTANCE SPACES
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Abstract
In this research paper, we have explored a novel form of distance known as the
T -distance within a b-metric space (Π, b, s), which is derived from the existing b-
metric on Π. Several examples illustrating this concept have been provided, along
with an examination of fixed point results using this notion. Furthermore, we have
presented an application of the T -distance in the context of fractional differential
equations.
References
Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund.
math, 3, 133–181.
Karapınar, E., & Fulga, A. (2023). Discussions on Proinov-Cb-Contraction Mapping on-Metric Space. Journal of Function Spaces, 2023(9), 1–10.
Karapınar, E., Romaguera, S., & Tirado, P. (2022). Characterizations of quasi-metric and G-metric completeness
involving ω-distances and fixed points. Demonstratio Mathematica, 55(1), 939–951.
Aydi, H., Karapinar, E., & Postolache, M. (2012). Tripled coincidence point theorems for weak Φ-contractions in partially ordered metric spaces, Fixed Point Theory Appl. 2012 44, https://doi.org/10.1186/1687-1812-2012-44.
Jleli, M., & Samet, B. (2014). A new generalization of the Banach contraction principle, Journal of inequalities and
applications, 2014 38, https://doi.org/10.1186/1029-242X-2014-38.
Bataihah, A., Qawasmeh, T.,& Shatnawi, M. (2022). Discussion on b-metric spaces and related results in metric and
G-metric spaces. Nonlinear Functional Analysis and Applications 27, no. 2, 233–247.
Shatanawi, W., Qawasmeh, T., Bataihah A., & Tallafha, A. (2021). New contractions and some fixed point results with
application based on extended quasi b-metric spaces, U.P.B. Sci. Bull., Series A, Vol. 83, Iss. 2 (2021) 1223–7027.
Qawasmeh, T., Shatanawi, W., Bataihah, A., & Tallafha, A. (2021). Fixed point results and (α, β)- triangular admis-
sibility in the frame of complete extended b-metric spaces and application, U.P.B. Sci. Bull., Series A, Vol. 83, no. 1 (2021): 113–124.
Abodayeh, K. Bataihah, A., & Shatanawi, W. (2017). Generalized Ω-distance mappings and some fixed point theorems,
U.P.B. Sci. Bull. Series A, 79 (2017): 223–232.
Abu-Irwaq, I., Shatanawi, W., Bataihah, A. & Nuseir, I. (2019). Fixed point results for nonlinear contractions with
generalized Ω-distance mappings, U.P.B. Sci. Bull. Series A 81, no. 1 (2019): 57–64.
Bakhtin, I.A. (1989). The contraction mapping principle in almost metric spaces. Funct. Anal., Gos. Ped. Inst.,
Unianowsk, 1989, 30, 26–37.
Jajarmi, A. & Baleanu, D. (2020) A new iterative method for the numerical solution of high-order non-linear fractional
boundary value problems, Front. Phys. 8:220. doi: 10.3389/fphy.2020.00220.
Adigüzel, R. S., Aksoy, Ü., Karapinar, E., & Erhan, I. M. (2020). On the solution of a boundary value problem asso-
ciated with a fractional differential equation, Mathematical Methods in the Applied Sciences, https://doi.org/10.1002/mma.6652
Afshari, H., Kalantari, S., & Karapinar, E. (2015) Solution of fractional differential equations via coupled fixed point,
Electron. J. Differ. Equ 286, no. 1 (2015): 2015.
Karapınar, E., Fulga, A., Rashid, M., Shahid, L., & Aydi, H. (2019). Large contractions on quasi-metric spaces with an
application to nonlinear fractional differential equations, Mathematics 7, no. 5 (2019): 444.
Alqahtani, B., Aydi, H., Karapınar, E., & Rakočević, V. (2019). A solution for Volterra fractional integral equations by
hybrid contractions. Mathematics 7, no. 8 (2019): 694.
Adıguzel, R. S., Aksoy, U., Karapınar, E., & Erhan, I. M. (2021). Uniqueness of solution for higher-order nonlinear
fractional differential equations with multi-point and integral boundary conditions, Revista de la Real Academia de
Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 115, no. 3 (2021): 155.
Adiguzel, R. S., Aksoy, U., Karapınar, E., and Erhan, I. M. (2021). On the solutions of fractional differential equations
via Geraghty type hybrid contractions, Appl. Comput. Math. 20(2), 313–333.
Afshari, H., Ahmadkhanlu, A. The existence of positive solutions for a Caputo-Hadamard boundary value problem
with an integral boundary condition, Advances in the Theory of Nonlinear Analysis and its Applications 7 No. 5,
–164. https://doi.org/10.17762/atnaa.v7.i5.332
Nosrati Sahlan, M., Afshari, H. (2024). The existence of solutions for some new boundary value problems involving the
q-derivative operator in quasi-b-metric and b-metric-like spaces, Lett. Nonlinear Anal. Appl., 2(2024) No.1.
Afshari, H., Roomi, V., Kalantari, S. (2022). The existence of the solutions of some inclusion problems involving caputo
and hadamard fractional derivatives by applying some new contractions, J. Nonlinear Convex Anal. 23(6), 1213–1229.
Afshari, H., Karapinar, E., (2021). A solution of the fractional differential equations in the setting of b-metric space,
Carpathian Math. Publ. 13(3), 764–774. doi:10.15330/cmp.13.3.764-774.
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