Fixed point theorem on $ CAT_{p}(0) $ metric spaces with applications in solving matrix equations and fractional differential equations

Mohammad Sajid; Lucas Wangwe; Hemanta Kalita; Santosh Kumar; Mohammad Sajid; Lucas Wangwe; Hemanta Kalita; Santosh Kumar

doi:10.3934/math.2025505

AIMS Mathematics

2025, Volume 10, Issue 5: 11131-11158. doi: 10.3934/math.2025505

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Fixed point theorem on $ CAT_{p}(0) $ metric spaces with applications in solving matrix equations and fractional differential equations

1.
Department of Mechanical Engineering, College of Engineering, Qassim University, Saudi Arabia
2.
Department of Mathematics, Mbeya University of Science and Technology, Tanzania
3.
Mathematics Division, VIT Bhopal University, Bhopal-Indore Highway, Kothrikalan, Sehore, Madhya Pradesh 466114, India
4.
Department of Mathematics, School of Physical Sciences, North-Eastern Hill University, Shillong-793022, Meghalaya, India

Received: 03 March 2025 Revised: 21 April 2025 Accepted: 06 May 2025 Published: 15 May 2025
MSC : 47H10, 54H25

This paper aimed to explore fixed point theorems for CMJ generalized mappings in $ CAT_{p}(0) $ metric spaces. To strengthen the established results, we presented a positive example. In applications, we found the existence of the solution to nonlinear matrix equations, and unique solutions of two scale fractal hybrid fractional differential equations in $ CAT_{p}(0) $.
- fixed point theorems,
- CMJ mappings,
- $ CAT_{p}(0) $ metric spaces,
- nonlinear matrix equation,
- fractional differential equations
Citation: Mohammad Sajid, Lucas Wangwe, Hemanta Kalita, Santosh Kumar. Fixed point theorem on $ CAT_{p}(0) $ metric spaces with applications in solving matrix equations and fractional differential equations[J]. AIMS Mathematics, 2025, 10(5): 11131-11158. doi: 10.3934/math.2025505

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Abstract

This paper aimed to explore fixed point theorems for CMJ generalized mappings in $ CAT_{p}(0) $ metric spaces. To strengthen the established results, we presented a positive example. In applications, we found the existence of the solution to nonlinear matrix equations, and unique solutions of two scale fractal hybrid fractional differential equations in $ CAT_{p}(0) $.

References

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