2008, ISBN 158488956X, xix, 680

Book

Filomat, ISSN 0354-5180, 1/2016, Volume 30, Issue 5, pp. 1315 - 1326

In this paper, we have established Hermite-Hadamard type inequalities for fractional integrals depending on a parameter.

Mathematical integrals | Mathematical inequalities | Mathematical functions | Riemann-Liouville fractional integral | Hermite-Hadamard’s inequalities | Integral inequalities | MATHEMATICS | Hermite-Hadamard's inequalities | MATHEMATICS, APPLIED | integral inequalities | DIFFERENTIABLE MAPPINGS

Mathematical integrals | Mathematical inequalities | Mathematical functions | Riemann-Liouville fractional integral | Hermite-Hadamard’s inequalities | Integral inequalities | MATHEMATICS | Hermite-Hadamard's inequalities | MATHEMATICS, APPLIED | integral inequalities | DIFFERENTIABLE MAPPINGS

Journal Article

3.
Full Text
The first integral method for Wu–Zhang system with conformable time-fractional derivative

Calcolo, ISSN 1126-5434, 2015, Volume 53, Issue 3, pp. 475 - 485

In this paper, the first integral method is used to construct exact solutions of the time-fractional Wu–Zhang system...

Wu–Zhang system | Numerical Analysis | Conformable fractional derivative | First integral method | 35Qxx | 35R11 | Mathematics | Theory of Computation | MATHEMATICS | Wu-Zhang system | EQUATION | CALCULUS | Methods | Algebra | Derivatives | Partial differential equations | Mathematical analysis | Integrals | Exact solutions | Nonlinearity | Rings (mathematics)

Wu–Zhang system | Numerical Analysis | Conformable fractional derivative | First integral method | 35Qxx | 35R11 | Mathematics | Theory of Computation | MATHEMATICS | Wu-Zhang system | EQUATION | CALCULUS | Methods | Algebra | Derivatives | Partial differential equations | Mathematical analysis | Integrals | Exact solutions | Nonlinearity | Rings (mathematics)

Journal Article

1993, ISBN 9782881248641, xxxvi, 976

Book

Journal of inequalities and applications, ISSN 1029-242X, 2019, Volume 2019, Issue 1, pp. 1 - 11

In current continuation, we have incorporated the notion of s−(α,m) $s- ( {\alpha,m} ) $-convex functions and have established new integral inequalities...

Simpson’s inequality | 26A51 | 26D10 | Analysis | Mathematics, general | Mathematics | Convex functions | Applications of Mathematics | 26A15 | Power-mean inequality | Riemann–Liouville fractional integral | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Liouville fractional integral | DIFFERENTIABLE MAPPINGS | HERMITE-HADAMARD | Simpson's inequality | REAL NUMBERS

Simpson’s inequality | 26A51 | 26D10 | Analysis | Mathematics, general | Mathematics | Convex functions | Applications of Mathematics | 26A15 | Power-mean inequality | Riemann–Liouville fractional integral | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Liouville fractional integral | DIFFERENTIABLE MAPPINGS | HERMITE-HADAMARD | Simpson's inequality | REAL NUMBERS

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 20

In this paper, a new general identity for differentiable mappings via k-fractional integrals is derived...

41A55 | ( h , m ) $(h,m)$ -convex functions | ( α , m ) $(\alpha,m)$ -convex functions | 26A51 | k -fractional integrals | 26D20 | Analysis | 26A33 | Mathematics, general | Mathematics | Applications of Mathematics | 26D07 | k-fractional integrals | (h, m) -convex functions | (α, m) -convex functions | MATHEMATICS | PREINVEX FUNCTIONS | MATHEMATICS, APPLIED | DIFFERENTIABLE MAPPINGS | QUASI-CONVEX | (alpha, m)-convex functions | CONVEX-FUNCTIONS | (h, m)-convex functions | S-CONVEX | DERIVATIVES | HERMITE-HADAMARD INEQUALITIES | Integrals | Inequalities | Convexity

41A55 | ( h , m ) $(h,m)$ -convex functions | ( α , m ) $(\alpha,m)$ -convex functions | 26A51 | k -fractional integrals | 26D20 | Analysis | 26A33 | Mathematics, general | Mathematics | Applications of Mathematics | 26D07 | k-fractional integrals | (h, m) -convex functions | (α, m) -convex functions | MATHEMATICS | PREINVEX FUNCTIONS | MATHEMATICS, APPLIED | DIFFERENTIABLE MAPPINGS | QUASI-CONVEX | (alpha, m)-convex functions | CONVEX-FUNCTIONS | (h, m)-convex functions | S-CONVEX | DERIVATIVES | HERMITE-HADAMARD INEQUALITIES | Integrals | Inequalities | Convexity

Journal Article

Mathematical and computer modelling, ISSN 0895-7177, 2013, Volume 57, Issue 9-10, pp. 2403 - 2407

In the present note, first we have established Hermite–Hadamard’s inequalities for fractional integrals...

Hermite–Hadamard’s inequalities | Integral inequalities | Riemann–Liouville fractional integral | Riemann-Liouville fractional integral | Hermite-Hadamard's inequalities | MATHEMATICS, APPLIED

Hermite–Hadamard’s inequalities | Integral inequalities | Riemann–Liouville fractional integral | Riemann-Liouville fractional integral | Hermite-Hadamard's inequalities | MATHEMATICS, APPLIED

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 6/2014, Volume 17, Issue 2, pp. 361 - 370

A family of generalized Erdélyi-Kober type fractional integrals is interpreted geometrically as a distortion of the rotationally invariant integral kernel of the Riesz fractional integral in terms of generalized Cassini ovaloids on R N...

Abstract Harmonic Analysis | Erdélyi-Kober fractional integrals | fractional calculus | Functional Analysis | Analysis | Mathematics | Riesz fractional integrals | Integral Transforms, Operational Calculus | generalized fractional calculus | Cassini ovaloids | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Erdelyi-Kober fractional integrals | Physics - General Physics

Abstract Harmonic Analysis | Erdélyi-Kober fractional integrals | fractional calculus | Functional Analysis | Analysis | Mathematics | Riesz fractional integrals | Integral Transforms, Operational Calculus | generalized fractional calculus | Cassini ovaloids | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Erdelyi-Kober fractional integrals | Physics - General Physics

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2017, Volume 2017, Issue 1, pp. 1 - 10

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named ( k , s ) $(k...

26A51 | Hermite-Hadamard inequality | generalized k -fractional integral | Analysis | 26A33 | Mathematics, general | ( k , s ) $(k, s)$ -fractional integral | Mathematics | Applications of Mathematics | ( k , s ) $(k, s)$ -Riemann-Liouville fractional integral | 26D15 | (k, s) -fractional integral | generalized k-fractional integral | (k, s) -Riemann-Liouville fractional integral | MATHEMATICS | MATHEMATICS, APPLIED | (k, s)-fractional integral | OPERATORS | (k, s)-Riemann-Liouville fractional integral | Integrals | Texts | Inequalities | documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(k, s)$\end{document}(k,s)-Riemann-Liouville fractional integral | Research | documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(k, s)$\end{document}(k,s)-fractional integral

26A51 | Hermite-Hadamard inequality | generalized k -fractional integral | Analysis | 26A33 | Mathematics, general | ( k , s ) $(k, s)$ -fractional integral | Mathematics | Applications of Mathematics | ( k , s ) $(k, s)$ -Riemann-Liouville fractional integral | 26D15 | (k, s) -fractional integral | generalized k-fractional integral | (k, s) -Riemann-Liouville fractional integral | MATHEMATICS | MATHEMATICS, APPLIED | (k, s)-fractional integral | OPERATORS | (k, s)-Riemann-Liouville fractional integral | Integrals | Texts | Inequalities | documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(k, s)$\end{document}(k,s)-Riemann-Liouville fractional integral | Research | documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(k, s)$\end{document}(k,s)-fractional integral

Journal Article

Journal of King Saud University - Science, ISSN 1018-3647, 10/2019, Volume 31, Issue 4, pp. 692 - 700

This paper presents two approximate methods such as Quadratic and Cubic approximations for the Riemann-Liouville fractional integral and Caputo fractional derivatives...

Quadratic scheme | Abel’s integral equations | Riemann-Liouville fractional integral | Cubic scheme | Caputo derivative | Abel's integral equations | NUMERICAL-SOLUTION | TRANSPORT | CALCULUS | MULTIDISCIPLINARY SCIENCES | SIMULATION

Quadratic scheme | Abel’s integral equations | Riemann-Liouville fractional integral | Cubic scheme | Caputo derivative | Abel's integral equations | NUMERICAL-SOLUTION | TRANSPORT | CALCULUS | MULTIDISCIPLINARY SCIENCES | SIMULATION

Journal Article

Journal of applied analysis, ISSN 1869-6082, 2018, Volume 24, Issue 2, pp. 211 - 221

In the present paper, the notion of generalized -preinvex Godunova–Levin function of second kind is introduced, and some new integral inequalities involving generalized -preinvex Godunova...

Simpson type inequality | Hölder’s inequality | 26A51 | Ostrowski type inequality | 26D10 | 26A33 | Hermite–Hadamard inequality | fractional integral | 26D07 | 26D15 | Hölder's inequality | Hermite-Hadamard inequality

Simpson type inequality | Hölder’s inequality | 26A51 | Ostrowski type inequality | 26D10 | 26A33 | Hermite–Hadamard inequality | fractional integral | 26D07 | 26D15 | Hölder's inequality | Hermite-Hadamard inequality

Journal Article

2016, Encyclopedia of mathematics and its applications, ISBN 1107111943, Volume 162, xvi, 383 pages

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal...

Calculus | Fractional calculus

Calculus | Fractional calculus

Book

Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering, ISSN 0959-6518, 2018, Volume 233, Issue 3, pp. 320 - 334

In this study, we deal with systems that can be represented by single fractional order pole models and propose an integer order proportional-integral/proportional-integral-derivative controller design...

liquid level control system | inverse control | pre-filtered integer order proportional–integral/proportional–integral controller | fractional order proportional–integral–derivative | Fractional order model | pre-filtered integer order proportional-integral/proportional-integral controller | DELAY SYSTEMS | PID CONTROLLERS | SINGLE | STABILITY | STABILIZATION | fractional order proportional-integral-derivative | NUMERICAL ALGORITHM | AUTOMATION & CONTROL SYSTEMS | Performance indices | Controllers | Design engineering | Design parameters | Approximation | Computer simulation | Control systems design | Transfer functions | Mathematical models | Proportional integral derivative

liquid level control system | inverse control | pre-filtered integer order proportional–integral/proportional–integral controller | fractional order proportional–integral–derivative | Fractional order model | pre-filtered integer order proportional-integral/proportional-integral controller | DELAY SYSTEMS | PID CONTROLLERS | SINGLE | STABILITY | STABILIZATION | fractional order proportional-integral-derivative | NUMERICAL ALGORITHM | AUTOMATION & CONTROL SYSTEMS | Performance indices | Controllers | Design engineering | Design parameters | Approximation | Computer simulation | Control systems design | Transfer functions | Mathematical models | Proportional integral derivative

Journal Article

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, ISSN 1578-7303, 04/2019, Volume 113, Issue 2, pp. 399 - 422

In this paper we will investigate the concept of the q-integral p-variation introduced in 1970's by Terehin...

MATHEMATICS | Integral variation | Nonlinear Hammerstein integral equation | 47H30 | Bounded variation | Superposition operator | Acting conditions | Fractional integral | Riemann-Liouville fractional integration | Primary 26A45 | Secondary 45G10 | 45G05

MATHEMATICS | Integral variation | Nonlinear Hammerstein integral equation | 47H30 | Bounded variation | Superposition operator | Acting conditions | Fractional integral | Riemann-Liouville fractional integration | Primary 26A45 | Secondary 45G10 | 45G05

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 14

In this paper, we obtain the Hermite–Hadamard type inequalities for s-convex functions and m-convex functions via a generalized fractional integral, known as Katugampola fractional integral, which is the generalization of Riemann...

26A51 | m -convex functions | 26D10 | 26A33 | Mathematics | Katugampola fractional integral | Riemann–Liouville fractional integral | s -convex functions | Hermite–Hadamard inequalities | Analysis | Mathematics, general | Convex functions | Applications of Mathematics | 26D07 | 26D15 | Hadamard fractional integral | s-convex functions | m-convex functions | Hermite-Hadamard inequalities | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Liouville fractional integral | HADAMARD-TYPE INEQUALITIES | Integrals | Convex analysis | Inequalities | Research

26A51 | m -convex functions | 26D10 | 26A33 | Mathematics | Katugampola fractional integral | Riemann–Liouville fractional integral | s -convex functions | Hermite–Hadamard inequalities | Analysis | Mathematics, general | Convex functions | Applications of Mathematics | 26D07 | 26D15 | Hadamard fractional integral | s-convex functions | m-convex functions | Hermite-Hadamard inequalities | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Liouville fractional integral | HADAMARD-TYPE INEQUALITIES | Integrals | Convex analysis | Inequalities | Research

Journal Article

Indian journal of physics, ISSN 0974-9845, 2013, Volume 88, Issue 2, pp. 177 - 184

In this paper, fractional derivatives in the sense of modified Riemann-Liouville derivative and first integral method are applied for constructing exact solutions of nonlinear fractional generalized...

Physics, general | Astrophysics and Astroparticles | Fractional generalized reaction duffing model | First integral method | Physics | Solitons | PHYSICS, MULTIDISCIPLINARY | SOLITON PERTURBATION-THEORY | KDV EQUATION | DIFFUSION | DE-VRIES EQUATION | EXPLICIT | Partial differential equations | Fractions

Physics, general | Astrophysics and Astroparticles | Fractional generalized reaction duffing model | First integral method | Physics | Solitons | PHYSICS, MULTIDISCIPLINARY | SOLITON PERTURBATION-THEORY | KDV EQUATION | DIFFUSION | DE-VRIES EQUATION | EXPLICIT | Partial differential equations | Fractions

Journal Article

Optical and Quantum Electronics, ISSN 0306-8919, 2018, Volume 50, Issue 3

In this paper, we propose the first integral method (FIM) and the improved tan(1/2 phi(xi))-expansion method (ITEM) for solving the density-dependent conformable fractional diffusion-reaction equation...

Improved tan(1/2 φ(ξ))-expansion method | First integral method | Density-dependent conformable fractional diffusion–reaction equation | Improved tan(1/2 phi(xi))-expansion Method | QUANTUM SCIENCE & TECHNOLOGY | OPTICS | Density-dependent conformable fractional diffusion-reaction equation | ENGINEERING, ELECTRICAL & ELECTRONIC

Improved tan(1/2 φ(ξ))-expansion method | First integral method | Density-dependent conformable fractional diffusion–reaction equation | Improved tan(1/2 phi(xi))-expansion Method | QUANTUM SCIENCE & TECHNOLOGY | OPTICS | Density-dependent conformable fractional diffusion-reaction equation | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2017, Volume 73, Issue 6, pp. 1346 - 1362

In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling...

Riemann–Liouville integral | Surface–volume reactions | Caputo fractional derivative | Fractional calculus | Abel integral equation | MATHEMATICS, APPLIED | SET | DIFFERENTIABILITY | GEOMETRIC INTERPRETATION | INTEGRODIFFERENTIAL CALCULUS | MODELS | DIFFUSION | Riemann-Liouville integral | DERIVATIVES | Surface-volume reactions

Riemann–Liouville integral | Surface–volume reactions | Caputo fractional derivative | Fractional calculus | Abel integral equation | MATHEMATICS, APPLIED | SET | DIFFERENTIABILITY | GEOMETRIC INTERPRETATION | INTEGRODIFFERENTIAL CALCULUS | MODELS | DIFFUSION | Riemann-Liouville integral | DERIVATIVES | Surface-volume reactions

Journal Article

Applicable analysis, ISSN 1563-504X, 2013, Volume 93, Issue 9, pp. 1846 - 1862

In this paper, a general integral identity for twice differentiable functions is derived...

Hermite-Hadamard inequality | Riemann-Liouville fractional integral | s-convex function | Simpson type inequalities | MATHEMATICS, APPLIED | Integrals | Estimates | Inequalities

Hermite-Hadamard inequality | Riemann-Liouville fractional integral | s-convex function | Simpson type inequalities | MATHEMATICS, APPLIED | Integrals | Estimates | Inequalities

Journal Article

Mechanics of Materials, ISSN 0167-6636, 03/2014, Volume 70, pp. 106 - 114

....•The suggested continuum equations describe fractional generalization of the gradient and integral elasticity...

Non-local media | Fractional derivatives | Fractional gradient elasticity | Long-range interaction | Lattice model | MECHANICS | MATERIALS SCIENCE, MULTIDISCIPLINARY | DYNAMICS | Physics - Materials Science

Non-local media | Fractional derivatives | Fractional gradient elasticity | Long-range interaction | Lattice model | MECHANICS | MATERIALS SCIENCE, MULTIDISCIPLINARY | DYNAMICS | Physics - Materials Science

Journal Article

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