Applied Mathematics & Information Sciences

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Inthisstudy,somefixed-point,coupled,tripled,andquadruplefixed-pointresultsforgeneralizedcontractivetypemappings under mild conditions in the setting of abstract spaces are obtained. Also, we established some solutions to integral equations, functional equations, functional Volterra-Fredholm integral equations, 2D Volterra integral equations, Riemann-Liouville integrals, Atangana- Baleanu integral operators, and the boundary value problem for singular coupled fractional differential equations are established. Moreover, a unique stationary distribution for the Markov process is discussed. Furthermore, a new faster iterative algorithm is created than the previous sober algorithms. The proposed algorithm is used to analyze convergence, stability, and data-dependence results. Finally, two numerical examples are also provided to highlight the behavior and effectiveness of our approach.

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