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Browsing by Author "Ali, Sajjad"

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    Article
    Citation Count: Ali, S...et al. (2019). "Computation of Iterative Solutions Along With Stability Analysis to A Coupled System of Fractional Order Differential Equations",Advances in Difference Equations, Vol. 2019, No. 1.
    Computation of Iterative Solutions Along With Stability Analysis to A Coupled System of Fractional Order Differential Equations
    (Springer International Publishing, 2019) Ali, Sajjad; Abdeljawad, Thabet; Shah, Kamal; Fahd Jarad; Arif, Muhammad; 234808
    In this research article, we investigate sufficient results for the existence, uniqueness and stability analysis of iterative solutions to a coupled system of the nonlinear fractional differential equations (FDEs) with highier order boundary conditions. The foundation of these sufficient techniques is a combination of the scheme of lower and upper solutions together with the method of monotone iterative technique. With the help of the proposed procedure, the convergence criteria for extremal solutions are smoothly achieved. Furthermore, a major aspect is devoted to the investigation of Ulam–Hyers type stability analysis which is also established. For the verification of our work, we provide some suitable examples along with their graphical represntation and errors estimates.
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    Article
    Citation Count: Ali, Sajjad; Shah, Kamal; Jarad, Fahd, "On stable iterative solutions for a class of boundary value problem of nonlinear fractional order differential equations", Mathematical Methods in the Applied Sciences, Vol. 42, No. 3, pp. 969-981, (2019).
    On stable iterative solutions for a class of boundary value problem of nonlinear fractional order differential equations
    (Wiley, 2019) Ali, Sajjad; Shah, Kamal; Jarad, Fahd; 234808
    In this article, sufficient conditions for the existence of extremal solutions to nonlinear boundary value problem (BVP) of fractional order differential equations (FDEs) are provided. By using the method of monotone iterative technique together with upper and lower solutions, conditions for the existence and approximation of minimal and maximal solutions to the BVP under consideration are constructed. Some adequate results for different kinds of Ulam stability are investigated. Maximum error estimates for the corresponding solutions are given as well. Two examples are provided to illustrate the results.