What does this research mean for the field?

A unique solution to a nonlinear fractional differential equation exists in non-Archimedean quasi-modular metric spaces. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to explore fixed points in non-Archimedean quasi-modular metric spaces and establish solutions for fractional differential equations.

March 8, 2026Open Access

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Solution of Fractional Differential Equations Using Orthogonal L−Simulation Contractions

Key Points

The aim is to explore fixed points in non-Archimedean quasi-modular metric spaces and establish solutions for fractional differential equations.
Utilized cyclic (α, β)-admissible mappings and orthogonal sets.
Employed ZY-simulation functions to demonstrate fixed points.
Expanded existing literature through generalization of findings.
Identified fixed points in non-Archimedean quasi-modular metric spaces.
Provided a unique solution to a nonlinear fractional differential equation.
Demonstrated practical applications through graphical representations.

Abstract

In this study, we unveil some outcomes in non‐Archimedean quasi‐modular metric spaces. By using cyclic ( α , β )−admissible mappings, orthogonal sets, and Z Y −simulation functions, we demonstrate the fixed point of a generalized orthogonal simulative contraction. Our results generalize and expand on analogous observations from the existing literature. We observe fixed points in a non‐Archimedean quasi‐modular metric space, with a graph as a practical application. In addition, we identify a unique solution to a nonlinear fractional differential equation. MSC 2020 Classification: 47H10; 54H25

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Solution of Fractional Differential Equations Using Orthogonal L−Simulation Contractions

Key Points

Abstract

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