Fixed-point theorems in complex-valued extended suprametric spaces with applications to fractional integro-differential equations

Amnah Essa Shammaky; Jamshaid Ahmad; Amnah Essa Shammaky; Jamshaid Ahmad

doi:10.3934/math.20261167

AIMS Mathematics

2026, Volume 11, Issue 9: 29365-29398. doi: 10.3934/math.20261167

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Research article

Fixed-point theorems in complex-valued extended suprametric spaces with applications to fractional integro-differential equations

Amnah Essa Shammaky ^{1
,},
Jamshaid Ahmad ^{2,3
,
,}

1.
Department of Mathematics, College of Science, Jazan University, P. O. Box 2097, Jazan 45142, Saudi Arabia; aeshamakhi@jazanu.edu.sa
2.
Department of Mathematics and Statistics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia; jkhan@uj.edu.sa
3.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria 0204, South Africa

Received: 11 February 2026 Revised: 21 August 2026 Accepted: 27 August 2026 Published: 11 September 2026
MSC : 34A08, 47H10, 54H25

The aim of this work is to introduce the concept of complex-valued extended suprametric spaces and to establish new common fixed-point results for cyclic and interpolative contractive mappings. The obtained theorems significantly extend and unify several well-known fixed-point results in complex-valued suprametric spaces, complex-valued metric spaces, and classical suprametric spaces as particular cases. To illustrate the effectiveness of the developed theory, nontrivial examples are provided. As an application of the main results, we study the existence and uniqueness of solutions to a nonlinear fractional integro-differential initial value problem involving the Atangana-Baleanu-Caputo derivative of order $ 0 < \alpha < 1 $ by employing fixed-point methods within the proposed complex-valued extended suprametric framework.
Citation: Amnah Essa Shammaky, Jamshaid Ahmad. Fixed-point theorems in complex-valued extended suprametric spaces with applications to fractional integro-differential equations[J]. AIMS Mathematics, 2026, 11(9): 29365-29398. doi: 10.3934/math.20261167

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Abstract

The aim of this work is to introduce the concept of complex-valued extended suprametric spaces and to establish new common fixed-point results for cyclic and interpolative contractive mappings. The obtained theorems significantly extend and unify several well-known fixed-point results in complex-valued suprametric spaces, complex-valued metric spaces, and classical suprametric spaces as particular cases. To illustrate the effectiveness of the developed theory, nontrivial examples are provided. As an application of the main results, we study the existence and uniqueness of solutions to a nonlinear fractional integro-differential initial value problem involving the Atangana-Baleanu-Caputo derivative of order $ 0 < \alpha < 1 $ by employing fixed-point methods within the proposed complex-valued extended suprametric framework.

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