Existence of a Solution to an Infinite System of Weighted Atangana-Baleanu Fractional Integral Equations via Measure of Non-Compactness on a Tempered Sequence Space
DOI:
https://doi.org/10.26713/cma.v16i3.3141Keywords:
Measure of Noncompactness (MNC), Fixed Point Theorems (FPT), Fractional Integral Equation (FIE)Abstract
The goal of this study is to investigate the existence of a solution of an infinite system of weighted Atangana-Baleanu fractional integral equations via a newly constructed generalised form of the Darbo’s fixed-point theorem on a tempered sequence space. Furthermore, an example has been illustrated to demonstrate the effectiveness of the result obtained.
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R. P. Agarwal, M. Meehan and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, x + 170 pages (2009).
M. Al-Refai, On weighted Atangana-Baleanu fractional operators, Advances in Difference Equations 2020 (2020), article number 3, DOI: 10.1186/s13662-019-2471-z.
A. H. Ansari, Note on φ-ψ contractive type mappings and related fixed point, in: Proceedings of the 2nd Regional Conference on Mathematics and Applications, Payeme Noor University, Iran, pp. 377 – 380 (2014).
R. Arab, H. K. Nashine, N. H. Can and T. T. Binh, Solvability of functional-integral equations (fractional order) using measure of noncompactness, Advances in Difference Equations 2020 (2020), article number 12, DOI: 10.1186/s13662-019-2487-4.
J. Bana´s and M. Krajewska, Existence of solutions for infinite systems of differential equations in spaces of tempered sequences, Electronic Journal of Differential Equations 2017(60) (2017), 1 – 28, URL: https://ejde.math.txstate.edu/Volumes/2017/60/banas.pdf.
J. Bana´s and M. Mursaleen, Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, New Delhi, xii + 315 pages (2014), DOI: 10.1007/978-81-322-1886-9.
J. Bana´s, M. Jleli, M. Mursaleen, B. Samet and C. Vetro, Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness, Springer, Singapore, xiii + 487 pages (2017), DOI: 10.1007/978-981-10-3722-1.
S. Beloul, M. Mursalem and A. H. Ansari, A generalization of Darbo’s fixed point theorem with an application to fractional integral equations, Journal of Mathematical Inequalities 15(3) (2021), 911 – 921, DOI: 10.7153/jmi-2021-15-63.
G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rendiconti del Seminario Matematico della Università di Padova 24 (1955), 84 – 92, URL: https://www.numdam.org/item/RSMUP_1955__24__84_0/.
A. Das, B. Hazarika and M. Mursaleen, Application of measure of noncompactness for solvability of the infinite system of integral equations in two variables in ℓp (1 < p <∞), Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113 (2019), 31 – 40, DOI: 10.1007/s13398-017-0452-1.
A. Das, B. Hazarika and P. Kumam, Some new generalization of Darbo’s fixed point theorem and its application on integral equations, Mathematics 7(3) (2019), 214, DOI: 10.3390/math7030214.
A. Das, B. Hazarika, R. Arab and M. Mursaleen, Applications of a fixed point theorem to the existence of solutions to the nonlinear functional integral equations in two variables, Rendiconti del Circolo Matematico di Palermo Series 2 68 (2019), 139 – 152, DOI: 10.1007/s12215-018-0347-9.
A. Das, B. Hazarika, V. Parvaneh and M. Mursaleen, Solvability of generalized fractional order integral equations via measures of noncompactness, Mathematical Sciences 15(3) (2021), DOI: 10.1007/s40096-020-00359-0.
A. Das, M. Paunovi´c, V. Parvaneh, M. Mursaleen and Z. Bagheri, Existence of a solution to an infinite system of weighted fractional integral equations of a function with respect to another function via a measure of noncompactness, Demonstratio Mathematica 56(1) (2023), 20220192, DOI: 10.1515/dema-2022-0192.
A. Das, R. Jain and H. K. Nashine, A fixed point result via new condensing operator and its application to a system of generalized proportional fractional integral equations, Journal of Pseudo-Differential Operators and Applications 14 (2023), article number 21, DOI: 10.1007/s11868-023-00519-5.
K. Kuratowski, Sur les espaces complets, Fundamenta Mathematicae 15(1) (1930), 301 – 309, URL: https://eudml.org/doc/212357.
M. Rabbani, A. Das, B. Hazarika and R. Arab, Existence of solution for two dimensional nonlinear fractional integral equation by measure of noncompactness and iterative algorithm to solve it, Journal of Computational and Applied Mathematics 370 (2020), 112654, DOI: 10.1016/j.cam.2019.112654.
M. Rabbani, A. Das, B. Hazarika and R. Arab, Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations, Chaos, Solitons & Fractals 140 (2020), 110221, DOI: 10.1016/j.chaos.2020.110221.
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