RESULTS ON TRICOMPLEX PARTIAL METRIC SPACES AND THEIR APPLICATION IN THE NONLINEAR BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

Zahia Mostefaoui (), Yahya Almalki (), Hala Abd-Elmageed and Mohamed Abdalla
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Zahia Mostefaoui: Laboratory of Nonlinear Partial Differential Equations and History of Mathematics, Department of Mathematics, ENS 16050, Vieux-Kouba, Algiers, Algeria
Yahya Almalki: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Hala Abd-Elmageed: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia4Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
Mohamed Abdalla: Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-9

Abstract: In the context of tricomplex analysis (TA), we present the tricomplex partial metric space (TPMS), which is a considerable advancement over the tricomplex metric space (TMS). This new approach provides for a more nuanced understanding of fixed point theorems, which is backed up by illustrative examples. Furthermore, fixed point theorems have been applied to nonlinear fractional boundary value issues.

Keywords: Tricomplex Numbers; Tricomplex Metric Space; Partial Metric Space; Common Fixed Point (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400882

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