Common Fixed-Points Technique for the Existence of a Solution to Fractional Integro-Differential Equations via Orthogonal Branciari Metric Spaces
Arul Joseph Gnanaprakasam,
Gunasekaran Nallaselli,
Absar Ul Haq,
Gunaseelan Mani,
Imran Abbas Baloch,
Kamsing Nonlaopon
Affiliations
Arul Joseph Gnanaprakasam
Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, India
Gunasekaran Nallaselli
Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, India
Absar Ul Haq
Department of Natural Sciences and Humanities, University of Engineering and Technology (Narowal Campus), Lahore 54000, Pakistan
Gunaseelan Mani
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India
Imran Abbas Baloch
Higher Education Department, Government Graduate College for Boys Gulberg, Punjab 54660, Pakistan
Kamsing Nonlaopon
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
The idea of symmetry is a built-in feature of the metric function. In this paper, we investigate the existence and uniqueness of a fixed point of certain contraction via orthogonal triangular α-orbital admissible mapping in the context of orthogonal complete Branciari metric spaces endowed with a transitive binary relation. Our results generalize and extend some pioneering results in the literature. Furthermore, the existence criteria of the solutions to fractional integro-differential equations are established to demonstrate the applicability of our results.
