An existence result involving both the generalized proportional Riemann-Liouville and Hadamard fractional integral equations through generalized Darbo's fixed point theorem

Rahul; Nihar Kumar Mahato; Sumati Kumari Panda; Manar A. Alqudah; Thabet Abdeljawad; Rahul; Nihar Kumar Mahato; Sumati Kumari Panda; Manar A. Alqudah; Thabet Abdeljawad

doi:10.3934/math.2022848

AIMS Mathematics

2022, Volume 7, Issue 8: 15484-15496. doi: 10.3934/math.2022848

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Research article

An existence result involving both the generalized proportional Riemann-Liouville and Hadamard fractional integral equations through generalized Darbo's fixed point theorem

1.
Department of Mathematics, IIITDM Jabalpur, India
2.
Department of Mathematics, GMR Institute of Technology, Rajam - 532 127, Andhra Pradesh, India
3.
Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia
4.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
5.
Department of Medical Research, China Medical University, 40402 Taichung, Taiwan

Received: 29 January 2022 Revised: 30 April 2022 Accepted: 13 May 2022 Published: 22 June 2022
MSC : 26A33, 26D15, 47H10

In this paper, we propose and prove an extension and generalization, which extends and generalizes the Darbo's fixed point theorem (DFPT) in the context of measure of noncompactness (MNC). Thereafter, we use DFPT to investigate the existence of solutions to mixed-type fractional integral equations (FIE), which include both the generalized proportional $ (\kappa, \tau) $-Riemann-Liouville and Hadamard fractional integral equations. We've included a suitable example to strengthen the article.
Citation: Rahul, Nihar Kumar Mahato, Sumati Kumari Panda, Manar A. Alqudah, Thabet Abdeljawad. An existence result involving both the generalized proportional Riemann-Liouville and Hadamard fractional integral equations through generalized Darbo's fixed point theorem[J]. AIMS Mathematics, 2022, 7(8): 15484-15496. doi: 10.3934/math.2022848

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Abstract

In this paper, we propose and prove an extension and generalization, which extends and generalizes the Darbo's fixed point theorem (DFPT) in the context of measure of noncompactness (MNC). Thereafter, we use DFPT to investigate the existence of solutions to mixed-type fractional integral equations (FIE), which include both the generalized proportional $ (\kappa, \tau) $-Riemann-Liouville and Hadamard fractional integral equations. We've included a suitable example to strengthen the article.

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