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Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 02/2018, Volume 154, pp. 129 - 144
In recent work, Elias and Hogancamp develop a recurrence for the Poincaré series of the triply graded Khovanov–Rozansky homology of certain links, one of which... 
Macdonald polynomials | Nabla operator | Khovanov–Rozansky homology | Torus links | Macdonald eigenoperators | MATHEMATICS | Khovanov-Rozansky homology | Cytokinins
Journal Article
Thermal Science, ISSN 0354-9836, 2018, Volume 22, Issue Suppl. 1, pp. S203 - S209
.... In this work, we also present new discrete fractional solutions of the modified Bessel dijferential equation by means of the nabla-discrete fractional calculus operator... 
Discrete fractional calculus | Modified Bessel equation | Nabla operator | modified Bessel equation | nabla operator | THERMODYNAMICS | discrete fractional calculus
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2011, Volume 34, Issue 18, pp. 2231 - 2241
We develop Cresson's nondifferentiable calculus of variations on the space of Hölder functions. Several quantum variational problems are considered: with and... 
quantum calculus | MATHEMATICS, APPLIED | Holder functions | calculus of variations | TIME SCALES | CALCULUS | Green's theorem | NOETHERS THEOREM | EQUATIONS | NABLA DERIVATIVES | RELATIVITY | Operators | Variational principles | Mathematical analysis | Calculus of variations | Independent variables
Journal Article
Gazi University Journal of Science, ISSN 1303-9709, 2016, Volume 29, Issue 2, pp. 467 - 472
Journal Article
Reports on mathematical physics, ISSN 0034-4877, 2017, Volume 80, Issue 1, pp. 11 - 27
.... We provide the integration by parts formula and we use the Q-operator to confirm our results... 
discrete exponential function | convolution | Caputo fractional difference | discrete nabla Laplace transform | Q-operator | PHYSICS, MATHEMATICAL | Mathematics - Dynamical Systems
Journal Article
THERMAL SCIENCE, ISSN 0354-9836, 2019, Volume 23, pp. S121 - S127
In this article, we also present new fractional solutions of the non-homogeneous and homogeneous non-Fuchsian differential equation by using nabla-discrete fractional calculus operator del(alpha) (0 < alpha < 1... 
nabla operator | CALCULUS OPERATOR | THERMODYNAMICS | OPTICAL SOLITONS | discrete fractional calculus | non-Fuchsian equations | Differential calculus | Fractional calculus | Differential equations
Journal Article
Mathematics (Basel), ISSN 2227-7390, 2018, Volume 6, Issue 12, p. 308
In this article, we obtain new fractional solutions of the general class of non-Fuchsian differential equations by using discrete fractional nabla operator ∇ η ( 0 < η < 1... 
Discrete fractional calculus | Fractional nabla operator | Non-Fuchsian equations | MATHEMATICS | fractional nabla operator | CALCULUS OPERATOR | discrete fractional calculus | non-Fuchsian equations
Journal Article
Journal of combinatorial theory. Series A, ISSN 0097-3165, 2019, Volume 163, pp. 182 - 194
The non-commutative five-term relation T1,0T0,1=T0,1T1,1T1,0 is shown to hold for certain operators acting on symmetric functions... 
Macdonald polynomials | Five-term relation | Nabla operator | Pieri rules | MATHEMATICS
Journal Article
Advances in difference equations, ISSN 1687-1847, 2013, Volume 2013, Issue 1, pp. 1 - 16
Journal Article
AIMS mathematics, ISSN 2473-6988, 2020, Volume 5, Issue 2, pp. 894 - 903
In the current article, we investigate the second order singular differential equation namely the effective mass Schrodinger equation by means of the fractional nabla operator... 
MATHEMATICS | MATHEMATICS, APPLIED | CALCULUS OPERATOR | discrete fractional | the nabla operator | the effective mass Schrodinger equation | the effective mass schrodinger equation
Journal Article
Applied mathematical modelling, ISSN 0307-904X, 2015, Volume 39, Issue 14, pp. 4180 - 4195
The main objective of this article is to provide a link between the solutions of an initial value problem of a linear singular system of fractional nabla... 
Linear discrete time system | Duality | Fractional nabla operator | Initial conditions | Difference equations | Singular systems | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | TIME | CONTROLLABILITY
Journal Article
Applied mathematics letters, ISSN 0893-9659, 2019, Volume 98, pp. 446 - 452
We investigate the connection between the sign of Δ1−μ+aνΔaμf(t) and the monotone behavior of t↦f(t). In particular, given a function f:Na→R we consider the... 
Discrete fractional calculus | Sequential fractional delta difference | Sharpness | Homotopy | Monotonicity | MATHEMATICS, APPLIED | CONVEXITY | NABLA
Journal Article
ISRAEL JOURNAL OF MATHEMATICS, ISSN 0021-2172, 03/2020, Volume 236, Issue 2, pp. 533 - 589
We utilize a new definition for the fractional delta operator and prove that it is equivalent by translation to the more commonly used operator... 
L(P)-MAXIMAL REGULARITY | MATHEMATICS | MAXIMAL REGULARITY | SPACES | DIFFERENCE-EQUATIONS | BOUNDARY-VALUE-PROBLEMS | LEBESGUE REGULARITY | NABLA | UNIQUENESS
Journal Article
Boundary value problems, ISSN 1687-2770, 2017, Volume 2017, Issue 1, pp. 1 - 23
...) Where t is an element of T = [nu - beta - 1, b + v - beta - 1]N nu-beta-1. Delta(beta)(v-2), b del(nu) are left and right fractional difference operators, respectively, and phi(p... 
positive solutions | boundary value problem | upper and lower solution | monotone iteration | discrete delta-nabla | fixed point theorem | MATHEMATICS | MATHEMATICS, APPLIED | Boundary value problems | Usage | Analysis | Laplacian operator | Operators | Approximation | Difference equations | Existence theorems | Mathematical analysis | Texts | Formulas (mathematics)
Journal Article
Filomat, ISSN 0354-5180, 2017, Volume 31, Issue 12, pp. 3671 - 3683
.... In this article, we use dual identities relating delta and nabla fractional difference operators to prove shortly the monotonicity properties for the (left Riemann... 
Dual identity | Q-operator | Right (left) delta and nabla Riemann and Caputo fractional differences | Right (left) delta and nabla fractional sums | MATHEMATICS | MATHEMATICS, APPLIED | dual identity | right (left) delta and nabla Riemann and Caputo fractional differences | right (left) delta and nabla fractional sums
Journal Article
Arab Journal of Mathematical Sciences, ISSN 1319-5166, 07/2017, Volume 23, Issue 2, pp. 157 - 172
...–Liouville and Caputo fractional differences, is considered. As a corollary, we provide an evidence to the fact that in case of right fractional differences, one has to mix between nabla and delta operators... 
Symmetric duality | Discrete fractional calculus | Summation by parts | The [formula omitted]-operator | Right (left) delta and nabla fractional sums | Right (left) delta and nabla fractional differences | Functions | Research | Functional equations | Mathematical research | Fractions | Mathematics - Classical Analysis and ODEs | The Q-operator
Journal Article
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