On deformable fractional order implicit differential equations involving orthogonal super metric spaces

Amit Gangwar; Shivam Rawat; Hassen Aydi; Saber Mansour; Amit Gangwar; Shivam Rawat; Hassen Aydi; Saber Mansour

doi:10.3934/math.2025653

AIMS Mathematics

2025, Volume 10, Issue 6: 14502-14514. doi: 10.3934/math.2025653

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Research article

On deformable fractional order implicit differential equations involving orthogonal super metric spaces

1.
Department of Mathematics, Bharat Institute of Engineering and Technology, Hyderabad, Telangana, India
2.
Department of Mathematics, H.N.B. Garhwal University, Srinagar(Garhwal)-246174, Uttarakhand, India
3.
Department of Mathematics, Graphic Era (Deemed to be) University, Dehradun, Uttarakhand, 248002, India
4.
Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
5.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
6.
Department of Mathematics, Umm Al-Qura University, Faculty of sciences, P.O. Box 14035, Holly Makkah 21955, Saudi Arabia

Received: 21 January 2025 Revised: 03 June 2025 Accepted: 19 June 2025 Published: 26 June 2025
MSC : 47H09, 47H10, 54H25

In this manuscript, we use the notion of orthogonality in a super metric space and prove some fixed point theorems that focus on orthogonal contractions and orthogonal $ \mathcal{F} $-contractions, which are types of mappings exhibiting particular contraction properties while satisfying orthogonality. To illustrate and support our theoretical results, we provide concrete examples that demonstrate the application of these findings. Furthermore, we show how our results can be utilized in practical scenarios by presenting a solution to a deformable implicit differential equation, highlighting the relevance of our work in both theoretical and applied contexts.
- orthogonal $ F $-contraction,
- orthogonal set,
- super metric space
Citation: Amit Gangwar, Shivam Rawat, Hassen Aydi, Saber Mansour. On deformable fractional order implicit differential equations involving orthogonal super metric spaces[J]. AIMS Mathematics, 2025, 10(6): 14502-14514. doi: 10.3934/math.2025653

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Abstract

In this manuscript, we use the notion of orthogonality in a super metric space and prove some fixed point theorems that focus on orthogonal contractions and orthogonal $ \mathcal{F} $-contractions, which are types of mappings exhibiting particular contraction properties while satisfying orthogonality. To illustrate and support our theoretical results, we provide concrete examples that demonstrate the application of these findings. Furthermore, we show how our results can be utilized in practical scenarios by presenting a solution to a deformable implicit differential equation, highlighting the relevance of our work in both theoretical and applied contexts.

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