Nabla discrete fractional calculus and nabla inequalities
نویسندگان
چکیده
منابع مشابه
Nabla discrete fractional calculus and nabla inequalities
Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincaré and Sobolev type inequalities .
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In this article, we propose the definition of one parameter matrix Mittag-Leffler functions of fractional nabla calculus and present three different algorithms to construct them. Examples are provided to illustrate the applicability of suggested algorithms.
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The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of nabla integrals. Here we propose a more general approach to the calculus of variations on time scales that allows to obtain both delta and nabla r...
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and Applied Analysis 3 Definition 2.2. Let ρ t t − 1 be the backward jump operator. Then i the nabla left fractional sum of order α > 0 starting from a is defined by ∇−α a f t 1 Γ α t ∑ s a 1 ( t − ρ s α−1f s , t ∈ Na 1 2.4 ii the nabla right fractional sum of order α > 0 ending at b is defined by b∇−αf t 1 Γ α b−1 ∑ s t ( s − ρ t α−1f s 1 Γ α b−1 ∑ s t σ s − t α−1f s , t ∈b−1 N. 2.5 We want to...
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Resat Yilmazer 1, Mustafa Inc 1,*, Fairouz Tchier 2 and Dumitru Baleanu 3,4 1 Department of Mathematics, Science Faculty, Fırat University, Elazığ 23119, Turkey; [email protected] 2 Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia; [email protected] 3 Department of Mathematics and Computer Science, Çankaya University, Ankara 06530, Turkey; dumitru...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2010
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2009.11.006