Results 251 to 260 of about 26,220 (280)

Discretized Fractional Calculus

SIAM Journal on Mathematical Analysis, 1986
Es werden für Fraktionalintegrale der Form \(\int^{x}_{0}(x- s)^{\alpha -1}x^{\beta -1}g(x)ds\) Konvolutionsquadraturen untersucht, d.h. numerische Näherungen in den Punkten \(x=0,h,2h,...Nh\) bestimmt. Es wird gezeigt, daß die angegebenen Methoden konvergent von der Ordnung p sind, wenn sie stabil und von der Ordnung p konsistent sind.
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Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus

Physica A: Statistical Mechanics and its Applications, 2018
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Huang, Lan-Lan, Baleanu, Dumitru, Mo, Zhi-Wen, Wu, Guo-Cheng   +3 more
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Initial value problems in discrete fractional calculus

Proceedings of the American Mathematical Society, 2008
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Atici, Ferhan M., Eloe, Paul W.
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Nonlocal BVPs and the Discrete Fractional Calculus

2015
In this chapter we discuss the concept of a nonlocal boundary value problem in the context of the discrete fractional calculus. More generally, we discuss how the nonlocal structure of the discrete fractional difference and sum operators affect their interpretation and analysis.
Christopher Goodrich, Allan C. Peterson
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About Discrete Fractional Calculus with Inequalities

2011
Here we define a Caputo like discrete fractional difference and we compare it to the earlier defined Riemann-Liouville fractional discrete analog. Then we present discrete fractional Taylor formulae and we estimate their remainders. Finally we give related discrete fractional Ostrowski, Poincare and Sobolev type inequalities.
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Multidimensional Discrete-Time Fractional Calculus of Variations

2015
In this paper a discrete-time multidimensional fractional calculus of variations is introduced. The fractional operators are defined in the sense of Gr\(\ddot{u}\)nvald–Letnikov. We derive necessary optimality conditions and then give examples illustrating the use of obtained results.
Agnieszka B. Malinowska, Tatiana Odzijewicz   +1 more
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Discrete Nabla Fractional Calculus with Inequalities

2011
Here we define a Caputo like discrete nabla fractional difference and we give discrete nabla fractional Taylor formulae. We estimate their remainders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincare and Sobolev type inequalities. This chapter relies on [51].
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Discrete Delta Fractional Calculus and Laplace Transforms

2015
At the outset of this chapter we will be concerned with the (delta) Laplace transform, which is a special case of the Laplace transform studied in the book by Bohner and Peterson [62]. We will not assume the reader has any knowledge of the material in that book. The delta Laplace transform is equivalent under a transformation to the Z-transform, but we
Christopher Goodrich, Allan C. Peterson
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Discrete Fractional Calculus

2015
Christopher Goodrich, Allan C. Peterson
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An eigenvalue problem in fractional h-discrete calculus

Fractional Calculus and Applied Analysis, 2022
Atıcı, F. M., Jonnalagadda, J. M.
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