Fractional Calculus and Applied Analysis, ISSN 1311-0454, 08/2016, Volume 19, Issue 4, pp. 806 - 831

... are only sketched. MSC 2010 : Primary 26A33; Secondary 33E12, 34A08, 34K37, 35R11 Key Words and Phrases: fractional calculus, Mittag-Leffler type func- tions, fractional...

fractional calculus | Primary 26A33 | noninstantaneous impulsive fractional differential equations | 35R11 | Mittag-Leffler type functions | Secondary 33E12 | 34K37 | fractional ordinary and partial differential equations | 34A08 | nonlocal impulsive fractional switched systems | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Boundary values | Solutions | Mathematical analysis | Differential equations

fractional calculus | Primary 26A33 | noninstantaneous impulsive fractional differential equations | 35R11 | Mittag-Leffler type functions | Secondary 33E12 | 34K37 | fractional ordinary and partial differential equations | 34A08 | nonlocal impulsive fractional switched systems | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Boundary values | Solutions | Mathematical analysis | Differential equations

Journal Article

SpringerPlus, ISSN 2193-1801, 12/2016, Volume 5, Issue 1, pp. 1 - 13

A new generalization of Struve function called generalized Galué type Struve function (GTSF) is defined and the integral operators involving Appell’s...

Primary 26A33 | Fractional kinetic equations | 44A10 | Science | Integral transforms | Secondary 33E12 | Generalized Struve function | 44A20 | Laplace transforms | Fractional calculus | Science, general | KINETIC-EQUATIONS | INTEGRATION | MULTIDISCIPLINARY SCIENCES | ASYMPTOTIC-EXPANSION | OPERATORS

Primary 26A33 | Fractional kinetic equations | 44A10 | Science | Integral transforms | Secondary 33E12 | Generalized Struve function | 44A20 | Laplace transforms | Fractional calculus | Science, general | KINETIC-EQUATIONS | INTEGRATION | MULTIDISCIPLINARY SCIENCES | ASYMPTOTIC-EXPANSION | OPERATORS

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2018, Volume 21, Issue 5, pp. 1377 - 1395

... results are deduced. MSC 2010 : Primary 26A33, 33E12; Secondary 26D10, 26D15 Key Words and Phrases: Mittag-Leffler function, Opial’s inequality, fractional calculus 1...

33E12 | fractional calculus | Primary 26A33 | Secondary 26D10 | Mittag-Leffler function | 26D15 | Opial’s inequality | Opial's inequality | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Operators (mathematics) | Arrays | Integrals

33E12 | fractional calculus | Primary 26A33 | Secondary 26D10 | Mittag-Leffler function | 26D15 | Opial’s inequality | Opial's inequality | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Operators (mathematics) | Arrays | Integrals

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2016, Volume 19, Issue 5, pp. 1105 - 1160

...: Primary 26A33; Secondary 33E12, 34A08, 26A48, 44A10, 91B74 Key Words and Phrases: fractional calculus, dielectric models, complete monotonicity, Mittag-Leffler...

fractional calculus | Mittag-Leffler functions | Primary 26A33 | 44A10 | Secondary 33E12 | differential operators | 26A48 | dielectric models | 91B74 | 34A08 | complete monotonicity | Differential operators | Complete monotonicity | Fractional calculus | Dielectric models | MATHEMATICS, APPLIED | ALPHA-RELAXATION | STRETCHED EXPONENTIAL FUNCTION | FRACTIONAL RELAXATION | DISPERSION | DIFFERENTIAL-EQUATIONS | WILLIAMS-WATTS | MATHEMATICS | ANOMALOUS DIFFUSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPERATORS | DERIVATIVES | Usage | Models | Dielectrics | Properties | Monotonic functions | Dielectric relaxation

fractional calculus | Mittag-Leffler functions | Primary 26A33 | 44A10 | Secondary 33E12 | differential operators | 26A48 | dielectric models | 91B74 | 34A08 | complete monotonicity | Differential operators | Complete monotonicity | Fractional calculus | Dielectric models | MATHEMATICS, APPLIED | ALPHA-RELAXATION | STRETCHED EXPONENTIAL FUNCTION | FRACTIONAL RELAXATION | DISPERSION | DIFFERENTIAL-EQUATIONS | WILLIAMS-WATTS | MATHEMATICS | ANOMALOUS DIFFUSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPERATORS | DERIVATIVES | Usage | Models | Dielectrics | Properties | Monotonic functions | Dielectric relaxation

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2017, Volume 20, Issue 5, pp. 1196 - 1215

Recently S. Gerhold and R. Garra – F. Polito independently introduced a new function related to the special functions of the Mittag-Leffler family. This...

Primary 33E12 | Mittag-Leffler and Wright functions | asymptotics | 30F15 | 35R11 | Secondary 30D10 | Laplace transforms | integral representation | special functions | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | LEFFLER | EXPONENTIAL ASYMPTOTICS | EXPANSION | Functions | Laplace transformation | Research | Functional equations | Mathematical research

Primary 33E12 | Mittag-Leffler and Wright functions | asymptotics | 30F15 | 35R11 | Secondary 30D10 | Laplace transforms | integral representation | special functions | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | LEFFLER | EXPONENTIAL ASYMPTOTICS | EXPANSION | Functions | Laplace transformation | Research | Functional equations | Mathematical research

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 12/2013, Volume 16, Issue 4, pp. 978 - 984

... for the nonexistence of real zeros of a certain Mittag–Leﬄer function. MSC 2010 : Primary: 34A08, 34A40; Secondary: 26D10, 34C10, 33E12 Key Words and Phrases: Lyapunov’s...

Abstract Harmonic Analysis | Functional Analysis | Analysis | Primary: 34A08, 34A40 | Mittag-Leffler function | fractional derivative, Green’s function | Secondary: 26D10, 34C10, 33E12 | Mathematics | Lyapunov’s inequality | Integral Transforms, Operational Calculus | fractional derivative, Green's function | Lyapunov's inequality | MATHEMATICS, APPLIED | fractional derivative | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Green's function

Abstract Harmonic Analysis | Functional Analysis | Analysis | Primary: 34A08, 34A40 | Mittag-Leffler function | fractional derivative, Green’s function | Secondary: 26D10, 34C10, 33E12 | Mathematics | Lyapunov’s inequality | Integral Transforms, Operational Calculus | fractional derivative, Green's function | Lyapunov's inequality | MATHEMATICS, APPLIED | fractional derivative | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Green's function

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 12/2013, Volume 16, Issue 4, pp. 802 - 815

... to the classical solutions is analyzed when α null 1 recovering the heat equation with its respective Stefan’s condition. MSC 2010 : Primary 26A33; Secondary 33E12, 35R11...

Abstract Harmonic Analysis | Functional Analysis | Primary 26A33 | Caputo’s fractional derivative | Analysis | fractional diffusion equation | Secondary 33E12, 35R11, 35R35, 35R37, 80A22 | Stefan’s problem | Mathematics | Integral Transforms, Operational Calculus | Caputo's fractional derivative | Stefan's problem | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Mathematics - Analysis of PDEs

Abstract Harmonic Analysis | Functional Analysis | Primary 26A33 | Caputo’s fractional derivative | Analysis | fractional diffusion equation | Secondary 33E12, 35R11, 35R35, 35R37, 80A22 | Stefan’s problem | Mathematics | Integral Transforms, Operational Calculus | Caputo's fractional derivative | Stefan's problem | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Mathematics - Analysis of PDEs

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2019, Volume 22, Issue 1, pp. 95 - 112

... 2018. MSC 2010 : Primary 65D20; Secondary 65D15, 33E12, 34A08, 33F05 Key Words and Phrases: discrete Mittag-Leffler function; numerical implementation; overflow...

33E12 | Secondary 65D15 | state transition matrix | Primary 65D20 | discrete Mittag-Leffler function | 33F05 | numerical implementation | overflow phenomenon | 34A08 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Mathematical analysis | Algorithms

33E12 | Secondary 65D15 | state transition matrix | Primary 65D20 | discrete Mittag-Leffler function | 33F05 | numerical implementation | overflow phenomenon | 34A08 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Mathematical analysis | Algorithms

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2018, Volume 21, Issue 1, pp. 10 - 28

We obtain a generalized diffusion equation in modified or Riemann-Liouville form from continuous time random walk theory. The waiting time probability density...

33E12 | Mittag-Leffler functions | Primary 26A33 | 35R11 | continuous time random walk (CTRW) | anomalous diffusion | generalized diffusion equation | Secondary 34A08 | LANGEVIN EQUATION | MATHEMATICS, APPLIED | SERIES | DISPERSION | PRABHAKAR | MATHEMATICS | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MODELS | Research | Heat equation | Random walks (Mathematics) | Mathematical research | Economic models | Mathematical analysis | Random walk | Random walk theory | Diffusion | Probability distribution functions | Probability density functions | Distribution functions

33E12 | Mittag-Leffler functions | Primary 26A33 | 35R11 | continuous time random walk (CTRW) | anomalous diffusion | generalized diffusion equation | Secondary 34A08 | LANGEVIN EQUATION | MATHEMATICS, APPLIED | SERIES | DISPERSION | PRABHAKAR | MATHEMATICS | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MODELS | Research | Heat equation | Random walks (Mathematics) | Mathematical research | Economic models | Mathematical analysis | Random walk | Random walk theory | Diffusion | Probability distribution functions | Probability density functions | Distribution functions

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 6/2013, Volume 16, Issue 2, pp. 297 - 316

In this paper, the Cauchy problem for the spatially one-dimensional distributed order diffusion-wave equation $\int_0^2 {p(\beta )D_t^\beta u(x,t)d\beta } =...

Primary 26A33 | probability density | completely monotone functions | Fourier transform | Mathematics | time-fractional diffusion-wave equation of distributed order | Integral Transforms, Operational Calculus | Stieltjes functions | Abstract Harmonic Analysis | Functional Analysis | complete Bernstein functions | Analysis | Secondary 33E12, 35S10, 45K05 | Bernstein functions | Laplace transform | Time-fractional diffusion-wave equation of distributed order | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CALCULUS | RELAXATION

Primary 26A33 | probability density | completely monotone functions | Fourier transform | Mathematics | time-fractional diffusion-wave equation of distributed order | Integral Transforms, Operational Calculus | Stieltjes functions | Abstract Harmonic Analysis | Functional Analysis | complete Bernstein functions | Analysis | Secondary 33E12, 35S10, 45K05 | Bernstein functions | Laplace transform | Time-fractional diffusion-wave equation of distributed order | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CALCULUS | RELAXATION

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2016, Volume 19, Issue 1, pp. 188 - 211

... of solutions on initial-boundary value conditions. MSC 2010: Primary 26A33; Secondary 33E12, 35S10, 45K05 Key Words and Phrases: maximum principles, fractional diffusion...

Riesz-Caputo fractional | fractional diffusion equations | Primary 26A33 | maximum principles | initial-boundary-value problems | 35S10 | Secondary 33E12 | 45K05 | variable-order fractional derivatives | Maximum principles | Initialboundary- value problems | Variable-order fractional derivatives | Riesz-caputo fractional | Fractional diffusion equations | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | BOUNDARY-VALUE PROBLEMS | Space and time | Inequalities (Mathematics) | Research | Mathematical research | Differential equations

Riesz-Caputo fractional | fractional diffusion equations | Primary 26A33 | maximum principles | initial-boundary-value problems | 35S10 | Secondary 33E12 | 45K05 | variable-order fractional derivatives | Maximum principles | Initialboundary- value problems | Variable-order fractional derivatives | Riesz-caputo fractional | Fractional diffusion equations | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | BOUNDARY-VALUE PROBLEMS | Space and time | Inequalities (Mathematics) | Research | Mathematical research | Differential equations

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2019, Volume 22, Issue 5, pp. 1284 - 1306

The paper [ ] by R. Garrappa, S. Rogosin, and F. Mainardi, entitled “On a generalized three-parameter Wright function of the Le Roy type” and published in ....

Primary 33E12 | special functions of fractional calculus | Mittag-Leffler functions of Le Roy type (MLR functions) | completely monotonic functions | Secondary 26A33 | 26A48 | 32A17 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Integers | Parameters | Laplace transforms | Arrays | Mathematics - Classical Analysis and ODEs

Primary 33E12 | special functions of fractional calculus | Mittag-Leffler functions of Le Roy type (MLR functions) | completely monotonic functions | Secondary 26A33 | 26A48 | 32A17 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Integers | Parameters | Laplace transforms | Arrays | Mathematics - Classical Analysis and ODEs

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 6/2014, Volume 17, Issue 2, pp. 371 - 381

... 33E12, 35R11, 35R35, 80A22 Key Words and Phrases: Caputo’s fractional derivative, fractional diffusion equation, Stefan’s problem 1. Introduction In 1695 L’Hopital...

Abstract Harmonic Analysis | Functional Analysis | Primary 26A33 | Secondary 33E12, 35R11, 35R35, 80A22 | Caputo’s fractional derivative | Analysis | fractional diffusion equation | Stefan’s problem | Mathematics | Integral Transforms, Operational Calculus | Caputo's fractional derivative | Stefan's problem | MOVING BOUNDARY-PROBLEMS | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Mathematics - Analysis of PDEs

Abstract Harmonic Analysis | Functional Analysis | Primary 26A33 | Secondary 33E12, 35R11, 35R35, 80A22 | Caputo’s fractional derivative | Analysis | fractional diffusion equation | Stefan’s problem | Mathematics | Integral Transforms, Operational Calculus | Caputo's fractional derivative | Stefan's problem | MOVING BOUNDARY-PROBLEMS | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Mathematics - Analysis of PDEs

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 6/2014, Volume 17, Issue 2, pp. 424 - 439

From the point of view of the general theory of the hyper-Bessel operators, we consider a particular operator that is suitable to generalize the standard...

Abstract Harmonic Analysis | fractional relaxation | Secondary 33E12, 34A08, 76A10 | fractional derivatives | Mittag-Leffler functions | Functional Analysis | Primary 26A33 | Analysis | hyper-Bessel differential operators | Mathematics | fractional power of operators | Integral Transforms, Operational Calculus | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DIFFERENTIAL-EQUATIONS

Abstract Harmonic Analysis | fractional relaxation | Secondary 33E12, 34A08, 76A10 | fractional derivatives | Mittag-Leffler functions | Functional Analysis | Primary 26A33 | Analysis | hyper-Bessel differential operators | Mathematics | fractional power of operators | Integral Transforms, Operational Calculus | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DIFFERENTIAL-EQUATIONS

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 02/2016, Volume 19, Issue 1, pp. 229 - 252

... order. Comparison is made with the use of Mikusinski operational calculus for solving similar problems. MSC 2010: Primary 26A33, 34A08; Secondary 33E12, 35R11...

Primary 26A33 | 35K90 | 35R11 | Secondary 33E12 | fundamental solutions | linear fractional differential equations with constant coefficients | 34A08 | Caputo derivatives | Cauchy problem | Fundamental solutions | Linear fractional differential equations with constant coefficients | Differential equations, Linear | Research | Mathematical research | Operator theory

Primary 26A33 | 35K90 | 35R11 | Secondary 33E12 | fundamental solutions | linear fractional differential equations with constant coefficients | 34A08 | Caputo derivatives | Cauchy problem | Fundamental solutions | Linear fractional differential equations with constant coefficients | Differential equations, Linear | Research | Mathematical research | Operator theory

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 04/2019, Volume 22, Issue 2, pp. 396 - 411

... analytic form for the form factors, the Debye function, and can study their asymptotic decay. MSC 2010 : Primary 60G22; Secondary 33E12, 26A33, 65R10 Key Words...

65R10 | Mittag-Leffler functions | 26A33 | generalized grey Brownian motion | Debye functions | Secondary 33E12 | structure factors | Primary 60G22 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | M-WRIGHT FUNCTION | DIFFUSION | Form factors | Gaussian process

65R10 | Mittag-Leffler functions | 26A33 | generalized grey Brownian motion | Debye functions | Secondary 33E12 | structure factors | Primary 60G22 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | M-WRIGHT FUNCTION | DIFFUSION | Form factors | Gaussian process

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 2015, Volume 18, Issue 1, pp. 146 - 162

... equations. MSC 2010: Primary 26A33; Secondary 33E12, 34A08, 34K37, 35R11 Key Words and Phrases: invariant subspace method, Mittag-Leer function, Kilbas-Saigo function...

Invariant subspace method | Kilbas-Saigo function | Regular α-singular point | α-analytic function | Mittag-Leffler function | α-ordinary point | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | alpha-ordinary point | regular alpha-singular point | alpha-analytic function | invariant subspace method | Invariant subspaces | Differential equations, Nonlinear | Difference equations | Differential equations, Partial | Analysis

Invariant subspace method | Kilbas-Saigo function | Regular α-singular point | α-analytic function | Mittag-Leffler function | α-ordinary point | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | alpha-ordinary point | regular alpha-singular point | alpha-analytic function | invariant subspace method | Invariant subspaces | Differential equations, Nonlinear | Difference equations | Differential equations, Partial | Analysis

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 3/2013, Volume 16, Issue 1, pp. 26 - 50

This survey concerns a causal elastic wave equation which implies frequency power-law attenuation. The wave equation can be derived from a fractional Zener...

fractional calculus | Primary 26A33 | acoustical wave equations | fractional viscoelasticity | elastic wave equations | Mathematics | Integral Transforms, Operational Calculus | Abstract Harmonic Analysis | Functional Analysis | fractional wave equations | Analysis | Secondary 33E12, 34A08, 34K37, 35L05, 92C50, 92C55, 35R11, 74J10 | fractional ordinary and partial differential equations | VISCOELASTIC MATERIALS | MATHEMATICS, APPLIED | DERIVATIVE MODEL | INHOMOGENEOUS-MEDIA | MAGNETIC-RESONANCE ELASTOGRAPHY | RHEOLOGICAL BEHAVIOR | LINEAR VISCOELASTICITY | PSEUDOSPECTRAL METHOD | MATHEMATICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | POWER-LAW ATTENUATION | MR ELASTOGRAPHY | ACOUSTIC PROPAGATION

fractional calculus | Primary 26A33 | acoustical wave equations | fractional viscoelasticity | elastic wave equations | Mathematics | Integral Transforms, Operational Calculus | Abstract Harmonic Analysis | Functional Analysis | fractional wave equations | Analysis | Secondary 33E12, 34A08, 34K37, 35L05, 92C50, 92C55, 35R11, 74J10 | fractional ordinary and partial differential equations | VISCOELASTIC MATERIALS | MATHEMATICS, APPLIED | DERIVATIVE MODEL | INHOMOGENEOUS-MEDIA | MAGNETIC-RESONANCE ELASTOGRAPHY | RHEOLOGICAL BEHAVIOR | LINEAR VISCOELASTICITY | PSEUDOSPECTRAL METHOD | MATHEMATICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | POWER-LAW ATTENUATION | MR ELASTOGRAPHY | ACOUSTIC PROPAGATION

Journal Article