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Browsing by Author "Ali, Arshad"

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    Article
    Citation Count: Ali, Arshad...et al. (2019). "Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations", Advances in Difference Equations.
    Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations
    (Springer Open, 2018) Ali, Arshad; Shah, Kamal; Jarad, Fahd; Gupta, Vidushi; Abdeljawad, Thabet; 234808
    In this paper, we study a coupled system of implicit impulsive boundary value problems (IBVPs) of fractional differential equations (FODEs). We use the Schaefer fixed point and Banach contraction theorems to obtain conditions for the existence and uniqueness of positive solutions. We discuss Hyers-Ulam (HU) type stability of the concerned solutions and provide an example for illustration of the obtained results.
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    Article
    Citation Count: Ali, Arshad...et al. (2020). "Mathematical analysis of nonlocal implicit impulsive problem under caputo fractional boundary conditions", Mathematical Problems in Engineering, Vol. 2020.
    Mathematical analysis of nonlocal implicit impulsive problem under caputo fractional boundary conditions
    (2020) Ali, Arshad; Gupta, Vidushi; Abdeljawad, Thabet; Shah, Kamal; Jarad, Fahd; 234808
    This paper is related to frame a mathematical analysis of impulsive fractional order differential equations (IFODEs) under nonlocal Caputo fractional boundary conditions (NCFBCs). By using fixed point theorems of Schaefer and Banach, we analyze the existence and uniqueness results for the considered problem. Furthermore, we utilize the theory of stability for presenting HyersUlam, generalized Hyers-Ulam, Hyers-Ulam-Rassias, and generalized Hyers-Ulam-Rassias stability results of the proposed scheme. Finally, some applications are offered to demonstrate the concept and results. The whole analysis is carried out by using Caputo fractional derivatives (CFDs). Copyright © 2020 Arshad Ali et al.
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    Article
    Citation Count: Ali, A.; Shah, K.; Baleanu, D., "Ulam stability results to a class of nonlinear implicit boundary value problems of impulsive fractional differential equations",Advances in Difference Equations, (January 2019).
    Ulam stability results to a class of nonlinear implicit boundary value problems of impulsive fractional differential equations
    (Pushpa Publishing House, 2019) Ali, Arshad; Shah, K.; Baleanu, Dumitru; 56389
    In this paper, we derive some sufficient conditions which ensure the existence and uniqueness of a solution for a class of nonlinear three point boundary value problems of fractional order implicit differential equations (FOIDEs) with some boundary and impulsive conditions. Also we investigate various types of Hyers-Ulam stability (HUS) for our concerned problem. Using classical fixed point theory and nonlinear functional analysis, we obtain the required conditions. In the last section we give an example to show the applicability of our obtained results.