Turkish Journal of Mathematics, ISSN 1300-0098, 2018, Volume 42, Issue 4, pp. 2000 - 2017

In this paper, the authors study some subordination and superordination properties for classes of p-valent meromorphic, analytic, and univalent functions...

Subordination properties | Integral operators | Analytic functions | P-valent meromorphic functions | Superordination properties | Univalent functions | Erdélyi-Kober-type integral operator | CRITERIA | subordination properties | PRESERVING SUBORDINATION | SUBCLASSES | univalent functions | MULTIPLIER TRANSFORMATIONS | Erdelyi-Kober-type integral operator | p-valent meromorphic functions | FAMILY | MATHEMATICS | UNIVALENT-FUNCTIONS | SUPERORDINATION | INCLUSION | superordination properties | integral operators

Subordination properties | Integral operators | Analytic functions | P-valent meromorphic functions | Superordination properties | Univalent functions | Erdélyi-Kober-type integral operator | CRITERIA | subordination properties | PRESERVING SUBORDINATION | SUBCLASSES | univalent functions | MULTIPLIER TRANSFORMATIONS | Erdelyi-Kober-type integral operator | p-valent meromorphic functions | FAMILY | MATHEMATICS | UNIVALENT-FUNCTIONS | SUPERORDINATION | INCLUSION | superordination properties | integral operators

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 08/2012, Volume 17, Issue 8, pp. 3129 - 3139

► Nonlinear integral equations involving in Erdélyi–Kober fractional operator are studied. ► Weakly singular integral inequalities are widely used. ► Novel...

Erdélyi–Kober fractional operator | Nonlinear integral equations | Existence and uniqueness | Local stability | Erdélyi-Kober fractional operator | EXISTENCE | MATHEMATICS, APPLIED | NEUTRAL DIFFERENTIAL-EQUATIONS | PHYSICS, FLUIDS & PLASMAS | EVOLUTION-EQUATIONS | PHYSICS, MATHEMATICAL | UNIQUENESS | Erdelyi-Kober fractional operator | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INFINITE DELAY | Operators | Closed balls | Computer simulation | Integral equations | Inequalities | Uniqueness | Nonlinearity | Mathematical models

Erdélyi–Kober fractional operator | Nonlinear integral equations | Existence and uniqueness | Local stability | Erdélyi-Kober fractional operator | EXISTENCE | MATHEMATICS, APPLIED | NEUTRAL DIFFERENTIAL-EQUATIONS | PHYSICS, FLUIDS & PLASMAS | EVOLUTION-EQUATIONS | PHYSICS, MATHEMATICAL | UNIQUENESS | Erdelyi-Kober fractional operator | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INFINITE DELAY | Operators | Closed balls | Computer simulation | Integral equations | Inequalities | Uniqueness | Nonlinearity | Mathematical models

Journal Article

Cogent Mathematics, ISSN 2331-1835, 01/2017, Volume 4, Issue 1

In this paper we examine the densities of a product and a ratio of two real positive definite matrix-variate random variables and , which are statistically...

Erdélyi-Kober operators | matrix-variate | densities | fractional integrals | pathway models | Operators (mathematics) | Random variables | Integrals | Density | Matrix methods

Erdélyi-Kober operators | matrix-variate | densities | fractional integrals | pathway models | Operators (mathematics) | Random variables | Integrals | Density | Matrix methods

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 12/2014, Volume 17, Issue 4, pp. 1215 - 1228

The reflection symmetric Erdélyi-Kober type fractional integral operators are used to construct fractional quasi-particle generators. The eigenfunctions and...

quasiparticle | Fock space | pairing-Hamiltonian | 26A33 | fractional operators | Mathematics | shifted Riesz integrals | Secondary: 70Hxx, 37Kxx, 81Q35, 81Q60 | Integral Transforms, Operational Calculus | Abstract Harmonic Analysis | Functional Analysis | Analysis | Erdélyi-Kober integrals | generalized fractional calculus | Quasiparticle | Generalized fractional calculus | Fractional operators | Shifted Riesz integrals | Pairing-Hamiltonian

quasiparticle | Fock space | pairing-Hamiltonian | 26A33 | fractional operators | Mathematics | shifted Riesz integrals | Secondary: 70Hxx, 37Kxx, 81Q35, 81Q60 | Integral Transforms, Operational Calculus | Abstract Harmonic Analysis | Functional Analysis | Analysis | Erdélyi-Kober integrals | generalized fractional calculus | Quasiparticle | Generalized fractional calculus | Fractional operators | Shifted Riesz integrals | Pairing-Hamiltonian

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2018, Volume 21, Issue 5, pp. 1360 - 1376

In this paper we investigate the extension of the multiple Erdélyi-Kober fractional integral operator of Kiryakova to arbitrary complex values of parameters by...

Secondary 33C60 | Primary 26A33 | multiple Erdélyi-Kober operator | Meijer’s | generalized hypergeometric function | 33C20 | function | Hadamard finite part | Meijer's G-function | GAMMA | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | INEQUALITIES | multiple Erdelyi-Kober operator | STIELTJES | Hypergeometric functions | Kernels | Operators (mathematics) | Regularization

Secondary 33C60 | Primary 26A33 | multiple Erdélyi-Kober operator | Meijer’s | generalized hypergeometric function | 33C20 | function | Hadamard finite part | Meijer's G-function | GAMMA | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | INEQUALITIES | multiple Erdelyi-Kober operator | STIELTJES | Hypergeometric functions | Kernels | Operators (mathematics) | Regularization

Journal Article

Far East Journal of Mathematical Sciences, ISSN 0972-0871, 2017, Volume 102, Issue 1, pp. 55 - 66

Fox-Wright function p Ψq | Pochhammer symbol | Generalized hypergeometric function p Fq | Riemann-Liouville fractional integral operators | Saigo fractional integral operators involving the Gauss hypergeometric function 2 F1 | Gamma function | Generalized k -Struve function | Erdélyi-Kober fractional integral operators | K -gamma function | K -Pochhammer symbol

Journal Article

Applied Mathematical Sciences, ISSN 1312-885X, 2015, Volume 9, Issue 69-72, pp. 3577 - 3591

Journal Article

Russian Mathematics, ISSN 1066-369X, 8/2017, Volume 61, Issue 8, pp. 22 - 35

We study the Cauchy problem for an equation with singular Bessel operator. Unlike traditional methods to solve this problem, we apply Erde´ lyi–Kober...

Mathematics, general | Mathematics | singular Bessel operator | polywave equation | Erdélyi–Kober operator | Cauchy problem

Mathematics, general | Mathematics | singular Bessel operator | polywave equation | Erdélyi–Kober operator | Cauchy problem

Journal Article

Filomat, ISSN 0354-5180, 2018, Volume 32, Issue 3, pp. 873 - 883

In this work we proved a composition of Lowndes' operator with differential operators of the high order, particularly, with iterated Bessel differential...

Generalized erdélyi-kober operator | Partial differential equations of the high order | Bessel differential operator | Lowndes operator | Cauchy problem | MATHEMATICS | MATHEMATICS, APPLIED | CAUCHY-PROBLEMS | partial differential equations of the high order | COEFFICIENTS | BOUNDEDNESS | Generalized Erdelyi-Kober operator

Generalized erdélyi-kober operator | Partial differential equations of the high order | Bessel differential operator | Lowndes operator | Cauchy problem | MATHEMATICS | MATHEMATICS, APPLIED | CAUCHY-PROBLEMS | partial differential equations of the high order | COEFFICIENTS | BOUNDEDNESS | Generalized Erdelyi-Kober operator

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 05/2014, Volume 233, pp. 439 - 444

The Lie symmetry analysis method is extended to deal with the time fractional KdV-type equation. It is shown that this equation can be reduced to an equation...

Riemann–Liouville derivative | Erdélyi–Kober operator | Fractional KdV-type equation | Lie symmetry analysis | Riemann-Liouville derivative | Erdélyi-Kober operator | ORDER | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | SYSTEMS | DIFFUSION EQUATION | Erdelyi-Kober operator

Riemann–Liouville derivative | Erdélyi–Kober operator | Fractional KdV-type equation | Lie symmetry analysis | Riemann-Liouville derivative | Erdélyi-Kober operator | ORDER | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | SYSTEMS | DIFFUSION EQUATION | Erdelyi-Kober operator

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 04/2020, Volume 83, p. 105108

Journal Article

SYMMETRY-BASEL, ISSN 2073-8994, 10/2019, Volume 11, Issue 10, p. 1281

The group classification of a class of time fractional generalized KdV equations with variable coefficient is presented. The Lie symmetry analysis method is...

initial and boundary value | Riemann-Liouville derivative | infinitesimal operator | MULTIDISCIPLINARY SCIENCES | Erdelyi-Kober operator | erdélyi-kober operator | riemann-liouville derivative

initial and boundary value | Riemann-Liouville derivative | infinitesimal operator | MULTIDISCIPLINARY SCIENCES | Erdelyi-Kober operator | erdélyi-kober operator | riemann-liouville derivative

Journal Article

Communications of the Korean Mathematical Society, ISSN 1225-1763, 2015, Volume 30, Issue 2, pp. 81 - 92

Journal Article

Panamerican Mathematical Journal, ISSN 1064-9735, 2012, Volume 22, Issue 3, pp. 117 - 145

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2017, Volume 40, Issue 1, pp. 255 - 273

In the present paper, our aim is to establish several formulas involving integral transforms, fractional derivatives, and a certain family of extended...

hypergeometric fractional derivatives | fox‐wright generalized hypergeometric function | Riemann–Liouville, Weyl, Erdélyi–Kober and other fractional derivative operators | generalized beta function | integral transforms | probability distributions | probability generating functions | Ramanujan's master theorem | extended generalized hypergeometric functions | probability density functions | fox-wright generalized hypergeometric function | MATHEMATICS, APPLIED | POCHHAMMER SYMBOLS | Riemann-Liouville, Weyl, Erdelyi-Kober and other fractional derivative operators | INCOMPLETE GAMMA-FUNCTIONS | GENERATING-FUNCTIONS | EXTENSION | FAMILY | BETA | OPERATORS | Distribution (Probability theory) | Hypergeometric functions | Integrals | Mathematical analysis | Transforms | Derivatives | Formulas (mathematics) | Probability density functions

hypergeometric fractional derivatives | fox‐wright generalized hypergeometric function | Riemann–Liouville, Weyl, Erdélyi–Kober and other fractional derivative operators | generalized beta function | integral transforms | probability distributions | probability generating functions | Ramanujan's master theorem | extended generalized hypergeometric functions | probability density functions | fox-wright generalized hypergeometric function | MATHEMATICS, APPLIED | POCHHAMMER SYMBOLS | Riemann-Liouville, Weyl, Erdelyi-Kober and other fractional derivative operators | INCOMPLETE GAMMA-FUNCTIONS | GENERATING-FUNCTIONS | EXTENSION | FAMILY | BETA | OPERATORS | Distribution (Probability theory) | Hypergeometric functions | Integrals | Mathematical analysis | Transforms | Derivatives | Formulas (mathematics) | Probability density functions

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2018, Volume 462, Issue 2, pp. 1425 - 1434

In this work we consider a nonlinear ordinary integro-differential equation which arises in the studies of time-fractional porous medium equation. The...

Time-fractional diffusion | Erdélyi–Kober operator | Existence and uniqueness | Porous medium | APPROXIMATE SOLUTIONS | SUBDIFFUSION EQUATIONS | MATHEMATICS, APPLIED | SIMILARITY SOLUTIONS | WATER-ABSORPTION | DIFFERENTIAL-EQUATIONS | POROUS BUILDING-MATERIALS | MATHEMATICS | ANOMALOUS DIFFUSION | TRANSPORT | RICHARDS EQUATION | MEDIA | Erdelyi-Kober operator | Differential equations

Time-fractional diffusion | Erdélyi–Kober operator | Existence and uniqueness | Porous medium | APPROXIMATE SOLUTIONS | SUBDIFFUSION EQUATIONS | MATHEMATICS, APPLIED | SIMILARITY SOLUTIONS | WATER-ABSORPTION | DIFFERENTIAL-EQUATIONS | POROUS BUILDING-MATERIALS | MATHEMATICS | ANOMALOUS DIFFUSION | TRANSPORT | RICHARDS EQUATION | MEDIA | Erdelyi-Kober operator | Differential equations

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 11/2018, Volume 41, Issue 16, pp. 6717 - 6725

In this paper, some classes of nonlinear partial fractional differential equations arising in some important physical phenomena are considered. Lie group...

symmetry analysis | Erdélyi‐Kober operator | generalized Burgers equation | exact solution | modified Riemann‐Liouville derivative | Fingero‐Imbibition phenomena | Fingero-Imbibition phenomena | Erdélyi-Kober operator | modified Riemann-Liouville derivative | MATHEMATICS, APPLIED | BURGERS | Erdelyi-Kober operator | Numerical analysis | Nonlinear equations | Partial differential equations | Computer simulation | Exact solutions | Group theory | Lie groups | Ordinary differential equations | Symmetry

symmetry analysis | Erdélyi‐Kober operator | generalized Burgers equation | exact solution | modified Riemann‐Liouville derivative | Fingero‐Imbibition phenomena | Fingero-Imbibition phenomena | Erdélyi-Kober operator | modified Riemann-Liouville derivative | MATHEMATICS, APPLIED | BURGERS | Erdelyi-Kober operator | Numerical analysis | Nonlinear equations | Partial differential equations | Computer simulation | Exact solutions | Group theory | Lie groups | Ordinary differential equations | Symmetry

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 10/2017, Volume 90, Issue 2, pp. 1105 - 1113

In this paper, symmetry properties and conservation laws of the (3+1) dimensional time-fractional modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equation have been...

Engineering | Vibration, Dynamical Systems, Control | New conservation law | Lie symmetries analysis | Classical Mechanics | (3+1) Dimensional time-fractional mKdV–ZK equation | Automotive Engineering | Mechanical Engineering | Erdélyi–Kober operator | Symmetry | Laws, regulations and rules | Analysis | Environmental law | Differential equations | Operators (mathematics) | Conservation laws | Acoustic properties | Ordinary differential equations | Acoustic waves

Engineering | Vibration, Dynamical Systems, Control | New conservation law | Lie symmetries analysis | Classical Mechanics | (3+1) Dimensional time-fractional mKdV–ZK equation | Automotive Engineering | Mechanical Engineering | Erdélyi–Kober operator | Symmetry | Laws, regulations and rules | Analysis | Environmental law | Differential equations | Operators (mathematics) | Conservation laws | Acoustic properties | Ordinary differential equations | Acoustic waves

Journal Article

Central European Journal of Physics, ISSN 1895-1082, 10/2013, Volume 11, Issue 10, pp. 1314 - 1336

In this paper some generalized operators of Fractional Calculus (FC) are investigated that are useful in modeling various phenomena and systems in the natural...

Environmental Physics | fractional calculus | operators of Riemann-Liouville and Caputo type | Cauchy problems | Physical Chemistry | integral transforms | Erdélyi-Kober operators | Geophysics/Geodesy | Biophysics and Biological Physics | Physics, general | Physics | special functions | ORDER | INTEGRAL TRANSFORM | PHYSICS, MULTIDISCIPLINARY | Erdelyi-Kober operators | GENERALIZED FRACTIONAL CALCULUS | DIFFERENTIAL-EQUATIONS | DIFFUSION

Environmental Physics | fractional calculus | operators of Riemann-Liouville and Caputo type | Cauchy problems | Physical Chemistry | integral transforms | Erdélyi-Kober operators | Geophysics/Geodesy | Biophysics and Biological Physics | Physics, general | Physics | special functions | ORDER | INTEGRAL TRANSFORM | PHYSICS, MULTIDISCIPLINARY | Erdelyi-Kober operators | GENERALIZED FRACTIONAL CALCULUS | DIFFERENTIAL-EQUATIONS | DIFFUSION

Journal Article

Computers & Mathematics with Applications, ISSN 0898-1221, 02/2020, Volume 79, Issue 4, pp. 1031 - 1048

Journal Article

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