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    Approximate solution of integral equations based on generalized sampling operators
    (Mehmet Yavuz, 2024) Usta, F.
    In this manuscript, we present and test a numerical scheme with an algorithm to solve Volterra and Abel’s integral equations utilizing generalized sampling operators. Illustrative computational examples are included to indicate the validity and practicability of the proposed technique. All of the computational examples in this research have been computed on a personal computer implementing some programs coded in MATLAB. © 2024 by the authors.
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    Bernstein operator method for approximate solution of singularly perturbed Volterra integral equations
    (Academic Press Inc., 2022) Usta, F.; Akyiğit, M.; Say, F.; Ansari, K. J.
    An approximate solution of integral equations takes an active role in the numerical analysis. This paper presents and tests an algorithm for the approximate solution of singularly perturbed Volterra integral equations via the Bernstein approximation technique. The method of computing the numerical approximation of the solution is properly demonstrated and exemplified in the matrix notation. Besides, the error bound and convergence associated with the numerical scheme are constituted. Finally, particular examples indicate the dependability and numerical capability of the introduced scheme in comparison with other numerical techniques. © 2021 Elsevier Inc.
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    On generalized the conformable fractional calculus
    (Isik University, 2019) Sarikaya, M. Z.; Budak, H.; Usta, F.
    In this paper, we generalize the conformable fractional derivative and integral and obtain several results such as the product rule, quotient rule, chain rule. © Işık University, Department of Mathematics, 2019; all rights reserved.
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    SOME GENERALIZED INTEGRAL INEQUALITIES VIA FRACTIONAL INTEGRALS
    (Comenius Univ, 2020) Sarikaya, M. Z.; Budak, H.; Usta, F.
    The main goal of this paper is to introduce a new integral definition concerned with fractional calculus. Then we establish generalized Hermite-Hadamard type integral inequalities for convex function using proposed fractional integrals. The results presented in this paper provide extensions of those given in earlier works.