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

Macdonald polynomials | Nabla operator | Khovanov–Rozansky homology | Torus links | Macdonald eigenoperators | MATHEMATICS | Khovanov-Rozansky homology | Cytokinins

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 17

...–Liouville (RL) fractional difference operator (a∇hαy)(t)>0 $({}_{a}\nabla_{h}^{\alpha }y)(t) > 0 $, then y(t) $y(t)$ is α-increasing. Conversely, if y(t) $y(t)$ is α...

Ordinary Differential Equations | Functional Analysis | Analysis | h -Discrete fractional mean value theorem | Difference and Functional Equations | Mathematics, general | Mathematics | Nabla h -Caputo fractional difference | Partial Differential Equations | Nabla Riemann–Liouville h -fractional difference | Nabla h-Caputo fractional difference | h-Discrete fractional mean value theorem | Nabla Riemann–Liouville h-fractional difference | MATHEMATICS, APPLIED | RIEMANN | DELTA | STABILITY | NABLA | INITIAL-VALUE PROBLEMS | CAPUTO | MATHEMATICS | KERNEL | INTEGRATION | Nabla Riemann-Liouville h-fractional difference | Operators (mathematics) | Boundary value problems | Furniture | Finite differences

Ordinary Differential Equations | Functional Analysis | Analysis | h -Discrete fractional mean value theorem | Difference and Functional Equations | Mathematics, general | Mathematics | Nabla h -Caputo fractional difference | Partial Differential Equations | Nabla Riemann–Liouville h -fractional difference | Nabla h-Caputo fractional difference | h-Discrete fractional mean value theorem | Nabla Riemann–Liouville h-fractional difference | MATHEMATICS, APPLIED | RIEMANN | DELTA | STABILITY | NABLA | INITIAL-VALUE PROBLEMS | CAPUTO | MATHEMATICS | KERNEL | INTEGRATION | Nabla Riemann-Liouville h-fractional difference | Operators (mathematics) | Boundary value problems | Furniture | Finite differences

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

Discrete fractional calculus | Modified Bessel equation | Nabla operator | modified Bessel equation | nabla operator | THERMODYNAMICS | discrete fractional calculus

Journal Article

Entropy, ISSN 1099-4300, 2016, Volume 18, Issue 2, p. 49

...) by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.

Discrete fractional calculus | Confluent hypergeometric equation | Nabla operator | confluent hypergeometric equation | THERMOELASTICITY | DIFFUSION | PHYSICS, MULTIDISCIPLINARY | discrete fractional calculus | Hypergeometric functions | Operators (mathematics) | Differential calculus | Ordinary differential equations | Fractional calculus | Differential equations

Discrete fractional calculus | Confluent hypergeometric equation | Nabla operator | confluent hypergeometric equation | THERMOELASTICITY | DIFFUSION | PHYSICS, MULTIDISCIPLINARY | discrete fractional calculus | Hypergeometric functions | Operators (mathematics) | Differential calculus | Ordinary differential equations | Fractional calculus | Differential equations

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2016, Volume 2016, Issue 1, pp. 1 - 31

In this article we discuss some of the qualitative properties of fractional difference operators...

26A51 | 26A33 | 39A06 | Mathematics | monotonicity | convexity | 39A30 | 39A99 | 39A10 | 39A12 | 39B99 | Mathematics, general | 26A48 | 34D05 | 39B62 | 39A22 | Ordinary Differential Equations | Functional Analysis | fractional initial value problem | Analysis | fractional difference calculus | Difference and Functional Equations | 39A60 | Partial Differential Equations | asymptotic behavior of solution | EXISTENCE | MATHEMATICS, APPLIED | CALCULUS | BOUNDARY-VALUE-PROBLEMS | NABLA | UNIQUENESS | MATHEMATICS | DISCRETE | SYSTEMS | Fractions | Monotonic functions | Differential equations | Tests, problems and exercises | Operators | Convexity | Difference equations | Asymptotic properties | Joints

26A51 | 26A33 | 39A06 | Mathematics | monotonicity | convexity | 39A30 | 39A99 | 39A10 | 39A12 | 39B99 | Mathematics, general | 26A48 | 34D05 | 39B62 | 39A22 | Ordinary Differential Equations | Functional Analysis | fractional initial value problem | Analysis | fractional difference calculus | Difference and Functional Equations | 39A60 | Partial Differential Equations | asymptotic behavior of solution | EXISTENCE | MATHEMATICS, APPLIED | CALCULUS | BOUNDARY-VALUE-PROBLEMS | NABLA | UNIQUENESS | MATHEMATICS | DISCRETE | SYSTEMS | Fractions | Monotonic functions | Differential equations | Tests, problems and exercises | Operators | Convexity | Difference equations | Asymptotic properties | Joints

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

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

7.
Spectral properties of schrodinger operator with a general boundary conditions on finite time scale

Gazi University Journal of Science, ISSN 1303-9709, 2016, Volume 29, Issue 2, pp. 467 - 472

Journal Article

Chaos, solitons and fractals, ISSN 0960-0779, 2019, Volume 126, pp. 315 - 324

In this article we define fractional difference operators with discrete generalized Mittag...

ABR Fractional difference | Discrete nabla Laplace transform | Convolution | AB Fractional sums | Iterated AB sum-differences | Discrete generalized Mittag–Leffler function | Higher order | ABC Fractional difference | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | Discrete generalized Mittag-Leffler function | MONOTONICITY ANALYSIS | PHYSICS, MATHEMATICAL

ABR Fractional difference | Discrete nabla Laplace transform | Convolution | AB Fractional sums | Iterated AB sum-differences | Discrete generalized Mittag–Leffler function | Higher order | ABC Fractional difference | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | Discrete generalized Mittag-Leffler function | MONOTONICITY ANALYSIS | PHYSICS, MATHEMATICAL

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

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

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

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

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

.... The first type relates nabla- and delta-type fractional sums and differences. The second type represented by the Q-operator relates left and right fractional sums and differences...

Ordinary Differential Equations | Functional Analysis | Analysis | right (left) delta and nabla Riemann | Difference and Functional Equations | Mathematics, general | Mathematics | dual identity | right (left) delta and nabla fractional sums | Partial Differential Equations | Q -operator | Dual identity | Right (left) delta and nabla Riemann | Q-operator | Right (left) delta and nabla fractional sums | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | Usage | Numerical analysis | Difference equations | Riemann integral | Inequalities (Mathematics) | Methods

Ordinary Differential Equations | Functional Analysis | Analysis | right (left) delta and nabla Riemann | Difference and Functional Equations | Mathematics, general | Mathematics | dual identity | right (left) delta and nabla fractional sums | Partial Differential Equations | Q -operator | Dual identity | Right (left) delta and nabla Riemann | Q-operator | Right (left) delta and nabla fractional sums | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | Usage | Numerical analysis | Difference equations | Riemann integral | Inequalities (Mathematics) | Methods

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

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

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

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

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)

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

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

20.
Full Text
Symmetric duality for left and right Riemann–Liouville and Caputo fractional differences

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

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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