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Fractal Fract
Volume 9
Issue 12
10.3390/fractalfract9120826
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Solving Riemann–Liouville Fractional Integral Equations by Fixed Point Results in Complex-Valued Suprametric Spaces

by
Hussain Gissy
1 and
Jamshaid Ahmad
2,*
1
Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
2
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria 0204, South Africa
*
Author to whom correspondence should be addressed.
Fractal Fract. 2025, 9(12), 826; https://doi.org/10.3390/fractalfract9120826
Submission received: 29 October 2025 / Revised: 6 December 2025 / Accepted: 9 December 2025 / Published: 18 December 2025
(This article belongs to the Section General Mathematics, Analysis)
Versions Notes

Abstract

Theaim of this research is to establish existence and uniqueness results for the Riemann–Liouville fractional integral equation of order αϰ(t)=f(t)+λΓα∫0tt−sα−1gs,ϰ(s)ds,t∈[0,1], by developing common fixed point theorems for generalized contractions involving control functions of two variables in the framework of complex valued suprametric spaces. The proposed results extend and generalize several existing findings in the literature, and some illustrative examples are provided to demonstrate the novelty and applicability of the main theorem.
Keywords: complex-valued suprametric spaces; common fixed point; Riemann–Liouville fractional integral equations; control functions complex-valued suprametric spaces; common fixed point; Riemann–Liouville fractional integral equations; control functions

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MDPI and ACS Style

Gissy, H.; Ahmad, J. Solving Riemann–Liouville Fractional Integral Equations by Fixed Point Results in Complex-Valued Suprametric Spaces. Fractal Fract. 2025, 9, 826. https://doi.org/10.3390/fractalfract9120826

AMA Style

Gissy H, Ahmad J. Solving Riemann–Liouville Fractional Integral Equations by Fixed Point Results in Complex-Valued Suprametric Spaces. Fractal and Fractional. 2025; 9(12):826. https://doi.org/10.3390/fractalfract9120826

Chicago/Turabian Style

Gissy, Hussain, and Jamshaid Ahmad. 2025. "Solving Riemann–Liouville Fractional Integral Equations by Fixed Point Results in Complex-Valued Suprametric Spaces" Fractal and Fractional 9, no. 12: 826. https://doi.org/10.3390/fractalfract9120826

APA Style

Gissy, H., & Ahmad, J. (2025). Solving Riemann–Liouville Fractional Integral Equations by Fixed Point Results in Complex-Valued Suprametric Spaces. Fractal and Fractional, 9(12), 826. https://doi.org/10.3390/fractalfract9120826

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