Regulated functions space R(R+,R∞) and its application to some infinite systems of fractional differential equations via family of measures of noncompactness-Reference-Cited by-同舟云学术

Regulated functions space R(R+,R∞) and its application to some infinite systems of fractional differential equations via family of measures of noncompactness

Published:2024 Issue:1 Volume:38 Page:135-146
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Amiri Kayvanloo Hojjatollah¹,Mursaleen Mohammad²,Allahyari Reza¹,Mehravaran Hamid¹,Allahyari Asghar³

Affiliation:

1. Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

2. Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan + Department of Mathematics, Aligarh Muslim University, Aligarh, India

3. Department of Mathematics, Tabas Branch, Islamic Azad University, Tabas, Iran

Abstract

We study the solvability of following infinite systems of fractional boundary value problem {cD?ui(t) = fi(t, ui(t))), ? ? (n ? 1, n), 0 < t < +?, ui(0) = 0, uq i (0) = 0, cD??1ui(?) = ?m?2,j=1 ?jui(?j). The purpose of this work is to present a new family of measures of noncompactness in the regulated function spaces R(R+,R?) on unbounded interval and a fixed point theorem of Darbo type. Finally, we give an example to show the effectiveness of the obtained result.

Publisher

National Library of Serbia

Reference25 articles.

1. R.P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications, Cambridge university press, vol. 141, 2001.

2. R. Allahyari, The behaviour of measures of noncompactness in L∞(Rn) with application to the solvability of functional integral equations, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 112(2)(2018) 561-573.

3. H. Amiri Kayvanloo, M. Khanehgir, R. Allahyari, A family of measures of noncompactness in the space Lp loc (RN) and its application to some nonlinear convolution type integral equations. Cogent Math. Stat. 6 (1)(2019), Art. ID 1592276, 13 pp.

4. H. Amiri Kayvanloo, M. Khanehgir, R. Allahyari, A family of measures of noncompactness in the Hölder space Cn,γ(R+) and its application to some fractional differential equations and numerical methods. J. Comput. Appl. Math. 363 (2020) 256-272.

5. H. Amiri Kayvanloo, M. Mursaleen, M. Mehrabinezhad, F. Pouladi Najafabadi Solvability of some fractional differential equations in the Hölder spaceHγ(R+) and their numerical treatment via measures of noncompactness. Mathematical Sciences, (2022), 1-11.