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Tytuł artykułu

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

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EN
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EN
In this article, some new generalizations of Darbo’s fixed-point theorem are given and the solvability of an infinite system of weighted fractional integral equations of a function with respect to another function is studied. Also, with the help of a proper example, we illustrate our findings.
Wydawca
Rocznik
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art. no. 20220192
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Department of Mathematics, Cotton University, Panbazar, Guwahati-781001, Assam, India
  • University of Kragujevac, Faculty of Hotel Management and Tourism, Vojvodjanska bb, 36210 Vrnjacka Banja, Serbia
  • Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran
  • Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung 40001, Taiwan
  • Department of Mathematics, Azadshahr Branch, Islamic Azad University, Azadshahr, Iran
Bibliografia
  • [1] K. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930), 301–309.
  • [2] G. Darbo, Punti uniti in trasformazioni a codominio non compatto (Italian), Rend. Sem. Mat. Univ. Padova 24 (1955), 84–92.
  • [3] A. Das, B. Hazarika, and P. Kumam, Some new generalization of Darbo’s fixed point theorem and its application on integral equations, Mathematics 7 (2019), no. 3, 214, DOI: https://doi.org/10.3390/math7030214.
  • [4] A. Das, B. Hazarika, V. Parvaneh, and M. Mursaleen, Solvability of generalized fractional order integral equations via measures of noncompactnes, Math. Sci. 15 (2021), no. 3, 241–251, DOI: https://doi.org/10.1007/s40096-020-00359-0.
  • [5] H. K. Nashine, R. W. Ibrahim, R. P. Agarwal, and N. H. Can, Existence of local fractional integral equation via a measure of non-compactness with monotone property on Banach spaces, Adv. Difference Equations 2020 (2020), 697, DOI: https://doi.org/10.1186/s13662-020-03153-3
  • [6] H. K. Nashine, R. W. Ibrahim, R. Arab, and M. Rabbani, Solvability of fractional dynamic systems utilizing measure of noncompactness, Nonlinear Anal. Model. Control 25 (2020), no. 4, 618–637, DOI: https://10.15388/namc.2020.25.17896.
  • [7] H. K. Nashine, R. W. Ibrahim, and N. H. Can, Solution of a fractal energy integral operator without body force using measure of noncompactness, Alex. Eng. J. 59 (2020), no. 6, 4101–4106, DOI: https://doi.org/10.1016/j.aej.2020.07.015.
  • [8] H. K. Nashine, R. W. Ibrahim, and C. C. Center, Solvability of a fractional Cauchy problem based on modified fixed point results of non-compactness measures, AIMS Math. 4 (2019), no. 3, 847–859, DOI: https://doi.org/10.3934/math.2019.3.847
  • [9] S. A. Mohiuddine, H. M. Srivastava, and A. Alotaibi, Application of measures of noncompactness to the infinite system of second-order differential equations in ℓp spaces, Adv. Difference Equations 2016 (2016), 317, DOI: https://doi.org/10.1186/s13662-016-1016-y
  • [10] J. Banaś and K. Goebel, Measure of noncompactness in Banach spaces, in: Lecture Notes in Pure and Applied Mathematics, vol. 60, Marcel Dekker, New York, 1980.
  • [11] J. Banaś and M. Krajewska, Existence of solutions for infinite systems of differential equations in spaces of tempered sequences, Electronic J. Differential Equations 60 (2017), 1–28.
  • [12] 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 Solit. Fractals 140 (2020), 110221, DOI: https://doi.org/10.1016/j.chaos.2020.110221.
  • [13] R. P. Agarwal and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge, United Kingdom, 2004.
  • [14] M. Mursaleen, Differential equations in classical sequence spaces, RACSAM 111 (2017), 587–612, DOI: https://doi.org/10.1007/s13398-016-0301-7.
  • [15] S. S. Chang and Y. J. Huang, Coupled fixed point theorems with applications, J. Korean Math. Soc. 33 (1996), no. 3, 575–585.
  • [16] F. Jarad, T. Abdeljawad, and K. Shah, On the weighted fractional operators of a function with respect to another function, Fractals 28 (2020), no. 8, 2040011, DOI: https://doi.org/10.1142/S0218348X20400113.
Typ dokumentu
Bibliografia
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