Yazar "Khan, Zareen A." seçeneğine göre listele

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    A greedy algorithm for partition of unity collocation method in pricing American options
    (Wiley, 2019) Fadaei, Yasin; Khan, Zareen A.; Akgul, Ali
    A greedy algorithm in combination with radial basis functions partition of unity collocation (GRBF-PUC) scheme is used as a locally meshless method for American option pricing. The radial basis function partition of unity method (RBF-PUM) is a localization technique. Because of having interpolation matrices with large condition numbers, global approximants and some local ones suffer from instability. To overcome this, a greedy algorithm is added to RBF-PUM. The greedy algorithm furnishes a subset of best nodes among the points X. Such nodes are then used as points of trial in a locally supported RBF approximant for each partition. Using of greedy selected points leads to decreasing the condition number of interpolation matrices and reducing the burdensome in pricing American options.
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    Öğe
    Qualitative Analysis of Stochastic Caputo-Katugampola Fractional Differential Equations
    (Mdpi, 2024) Khan, Zareen A.; Liaqat, Muhammad Imran; Akgul, Ali; Conejero, J. Alberto
    Stochastic pantograph fractional differential equations (SPFDEs) combine three intricate components: stochastic processes, fractional calculus, and pantograph terms. These equations are important because they allow us to model and analyze systems with complex behaviors that traditional differential equations cannot capture. In this study, we achieve significant results for these equations within the context of Caputo-Katugampola derivatives. First, we establish the existence and uniqueness of solutions by employing the contraction mapping principle with a suitably weighted norm and demonstrate that the solutions continuously depend on both the initial values and the fractional exponent. The second part examines the regularity concerning time. Third, we illustrate the results of the averaging principle using techniques involving inequalities and interval translations. We generalize these results in two ways: first, by establishing them in the sense of the Caputo-Katugampola derivative. Applying condition beta=1, we derive the results within the framework of the Caputo derivative, while condition beta -> 0+ yields them in the context of the Caputo-Hadamard derivative. Second, we establish them in Lp space, thereby generalizing the case for p=2.
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    Öğe
    Revised and Generalized Results of Averaging Principles for the Fractional Case
    (Mdpi, 2024) Liaqat, Muhammad Imran; Khan, Zareen A.; Conejero, J. Alberto; Akgul, Ali
    The averaging principle involves approximating the original system with a simpler system whose behavior can be analyzed more easily. Recently, numerous scholars have begun exploring averaging principles for fractional stochastic differential equations. However, many previous studies incorrectly defined the standard form of these equations by placing epsilon in front of the drift term and epsilon in front of the diffusion term. This mistake results in incorrect estimates of the convergence rate. In this research work, we explain the correct process for determining the standard form for the fractional case, and we also generalize the result of the averaging principle and the existence and uniqueness of solutions to fractional stochastic delay differential equations in two significant ways. First, we establish the result in Lp space, generalizing the case of p=2. Second, we establish the result using the Caputo-Katugampola operator, which generalizes the results of the Caputo and Caputo-Hadamard derivatives.