Results 21 to 30 of about 374,024 (252)
Grundwald-Letnikov Operator and Its Role in Solving Fractional Differential Equations [PDF]
, 2022 Leibnitz in 1663 introduced the derivative notation for the order of natural numbers, and then the idea of fractional derivatives appeared. Only a century later, this idea began to be realized with the discovery of the concepts of fractional derivatives ...
Parmikanti, Kankan, Rusyaman, Endang
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Numerical approach of riemann-liouville fractional derivative operator
International Journal of Electrical and Computer Engineering (IJECE), 2021 <p>This article introduces some new straightforward and yet powerful formulas in the form of series solutions together with their residual errors for approximating the Riemann-Liouville fractional derivative operator. These formulas are derived by utilizing some of forthright computations, and by utilizing the so-called weighted mean value ...
Ramzi B. Albadarneh +4 more
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Numerical Linear Algebra with Applications, Volume 30, Issue 1, January 2023., 2023 Abstract In this work, we focus on a fractional differential equation in Riesz form discretized by a polynomial B‐spline collocation method. For an arbitrary polynomial degree p$$ p $$, we show that the resulting coefficient matrices possess a Toeplitz‐like structure. We investigate their spectral properties via their symbol and we prove that, like for
Mariarosa Mazza +3 more
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Reconstructing volatility: Pricing of index options under rough volatility
Mathematical Finance, Volume 33, Issue 1, Page 19-40, January 2023., 2023 Abstract Avellaneda et al. (2002, 2003) pioneered the pricing and hedging of index options – products highly sensitive to implied volatility and correlation assumptions – with large deviations methods, assuming local volatility dynamics for all components of the index.
Peter K. Friz, Thomas Wagenhofer
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A new Definition of Fractional Derivative and Fractional Integral [PDF]
Kirkuk Journal of Science, 2018 In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed.
Ahmed M. Kareem
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On the k-Riemann-Liouville fractional derivative
International Journal of Contemporary Mathematical Sciences, 2013 The aim of this paper is to introduce an alternative denition for the k-Riemann-Liouville fractional derivative given in [6] and whose advantage is that it is the left inverse of the corresponding of k-RiemannLiouville fractional integral operator introduced by [5].
Luis Guillermo Romero +3 more
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Fractional Sobolev Spaces via Riemann-Liouville Derivatives [PDF]
Journal of Function Spaces and Applications, 2013 Using Riemann-Liouville derivatives, we introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones. Next, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and compactness of some imbeddings ...
Dariusz Idczak, Stanisław Walczak
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Fractional boundary value problems with Riemann-Liouville fractional derivatives [PDF]
Advances in Difference Equations, 2015 In this paper, by employing two fixed point theorems of a sum operators, we investigate the existence and uniqueness of positive solutions for the following fractional boundary value problems: $-D_{0+}^{\alpha}x(t)=f(t, x(t),
Caozong Cheng, Jingjing Tan
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Generalized Extended Riemann-Liouville Type Fractional Derivative Operator
Kragujevac Journal of Mathematics, 2023 In this paper, we present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [?]. Some recurrence relations, transformation formulas, Mellin transform and integral representations are obtained for these ...
Abbas, Hafida +3 more
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Approximation with Riemann-Liouville fractional derivatives [PDF]
Studia Universitatis Babes-Bolyai Matematica, 2019 n this article we study quantitatively with rates the pointwise convergence of a sequence of positive sublinear operators to the unit operator over continuous functions. This takes place under low order smothness,less than one, of the approximated function and it is expressed via the left and right Riemann-Liouville fractional derivatives of it.
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