Zhou et al. Journal of Inequalities and Applications (2022) 2022:148 https://doi.org/10.1186/s13660-022-02887-w RESEARCH Open Access Solution of fractional integral equations via fixed point results Mi Zhou 1,2,3,4 , Naeem Saleem 5* and Shahid Bashir 6 * Correspondence: naeem.saleem2@gmail.com 5 Department of Mathematics, University of Management and Technology, Lahore, Pakistan Full list of author information is available at the end of the article Abstract In this paper, we introduce two new concepts of F-contraction, called dual F ∗ -weak contraction and triple F ∗ -weak contraction, which generalize the existing contractions in the sense of Wardowski, Jleli and Samet as well as Skof. These new generalizations embed their roots in the aim devoted to extending the generalized Banach contraction conjuncture to the class of F-contraction type mappings with the use of multiple F-type functions. Furthermore, we establish the existence of a unique fixed point for such contractions under certain conditions. Fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates that can be expressed as functions of one independent variable. We apply our main result to weaken certain conditions on the fractional integral equations. Finally, we discuss the significance of our obtained results in comparison with certain renowned ones in the literature. MSC: 47H10; 47H19; 54H25 Keywords: Dual F ∗ -weak contraction; Triple F ∗ -weak contraction; F-contraction; Fixed point; Fractional integral equations 1 Introduction and preliminaries In a plethora of real and theoretical world problems, the existence of the solution to a problem is equivalent to the existence of a fixed point. Therefore, fixed points are of phe- nomenal importance in different areas of science and have become the subject of scientific research. Metric fixed point theory was initiated by Banach [1] with a principle known as Banach contraction principle. Banach established a remarkable fixed point theorem for a contraction F : X → X in a metric space (X, d) by introducing the following contraction condition: d(Fx, Fy) ≤ kd(x, y) for all k ∈ [0, 1), x, y ∈ X. (1) Over the years, the Banach contraction principle has been generalized in numerous direc- tions. In most of the generalizations, either the topology is weakened or the contractive nature of the mapping is weakened (for example, see [2–15] etc.). The aim of this research is to establish some interesting results concerning new general- izations or extensions of the Banach contraction principle. The idea behind this research © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.