2018, 1, ISBN 9781315167183, Volume 1, xxxvii, 273 pages

The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in...

Wavelets (Mathematics) | Fractional differential equations | Differential equations, Partial | Numerical solutions | Differential equations | Differential Equations | Applied Mathematics | Mathematical Physics | Computational Numerical Analysis

Wavelets (Mathematics) | Fractional differential equations | Differential equations, Partial | Numerical solutions | Differential equations | Differential Equations | Applied Mathematics | Mathematical Physics | Computational Numerical Analysis

Book

2017, 1, ISBN 1498764835, xii, 264 pages

The book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional...

Impulsive differential equations | Mathematical Modeling | Applied Mathematics | Differential Equations | Fractional differential equations

Impulsive differential equations | Mathematical Modeling | Applied Mathematics | Differential Equations | Fractional differential equations

Book

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 07/2017, Volume 48, pp. 509 - 519

In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order...

Fractional couple Burgers equation | (N+1)-dimensional fractional reduced DTM | Fractional Zakharovâ€“Kuznetsov equation | Fractional wave like problem | Fractional calculus | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | HOMOTOPY PERTURBATION METHOD | PHYSICS, MATHEMATICAL | HEAT-LIKE | VARIATIONAL ITERATION METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | WAVE-LIKE EQUATIONS | Fractional Zakharov-Kuznetsov equation | SYSTEMS | Methods | Differential equations

Fractional couple Burgers equation | (N+1)-dimensional fractional reduced DTM | Fractional Zakharovâ€“Kuznetsov equation | Fractional wave like problem | Fractional calculus | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | HOMOTOPY PERTURBATION METHOD | PHYSICS, MATHEMATICAL | HEAT-LIKE | VARIATIONAL ITERATION METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | WAVE-LIKE EQUATIONS | Fractional Zakharov-Kuznetsov equation | SYSTEMS | Methods | Differential equations

Journal Article

1999, Mathematics in science and engineering, ISBN 0125588402, Volume 198, 366

This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the...

Numerical solutions | Fractional calculus | Differential equations | Fractions

Numerical solutions | Fractional calculus | Differential equations | Fractions

eBook

2016, ISBN 9780128042779, x, 283 pages

Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much...

Evolution equations | Differential inclusions | Mathematics | Fractional differential equations

Evolution equations | Differential inclusions | Mathematics | Fractional differential equations

Book

6.
Full Text
Fuzzy Arbitrary Order System

: Fuzzy Fractional Differential Equations and Applications

2016, ISBN 9781119004233, 275

Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical...

Fractional differential equations | Fuzzy mathematics | Differential equations

Fractional differential equations | Fuzzy mathematics | Differential equations

eBook

Applied Mathematics and Computation, ISSN 0096-3003, 11/2018, Volume 336, pp. 433 - 453

In this paper, we consider a new fractional function based on Legendre and Laguerre polynomials for solving a class of linear and nonlinear time-space...

Pseudo-operational matrix of integration | Operational matrix of integration | Fractional partial differential equation | Fractional-order Legendreâ€“Laguerre functions | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | COLLOCATION METHOD | INTEGRATION | CALCULUS | Fractional-order Legendre-Laguerre functions | WAVELET OPERATIONAL MATRIX | Differential equations

Pseudo-operational matrix of integration | Operational matrix of integration | Fractional partial differential equation | Fractional-order Legendreâ€“Laguerre functions | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | COLLOCATION METHOD | INTEGRATION | CALCULUS | Fractional-order Legendre-Laguerre functions | WAVELET OPERATIONAL MATRIX | Differential equations

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 59, Issue 3, pp. 1326 - 1336

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For...

Operational matrix | Legendre polynomials | Collocation method | Caputo derivative | Fractional-order differential equations | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | APPROXIMATE | CALCULUS

Operational matrix | Legendre polynomials | Collocation method | Caputo derivative | Fractional-order differential equations | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | APPROXIMATE | CALCULUS

Journal Article

9.
Full Text
Fractional-order Legendre functions for solving fractional-order differential equations

Applied Mathematical Modelling, ISSN 0307-904X, 04/2013, Volume 37, Issue 7, pp. 5498 - 5510

In this article, a general formulation for the fractional-order Legendre functions (FLFs) is constructed to obtain the solution of the fractional-order...

Operational matrix | Tau method | Fractional-order Legendre functions | Fractional-order differential equations | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | HOMOTOPY PERTURBATION METHOD | Analysis | Differential equations | Mathematical analysis | Orthogonal functions | Legendre functions | Mathematical models | Calculus | Polynomials | Derivatives

Operational matrix | Tau method | Fractional-order Legendre functions | Fractional-order differential equations | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | HOMOTOPY PERTURBATION METHOD | Analysis | Differential equations | Mathematical analysis | Orthogonal functions | Legendre functions | Mathematical models | Calculus | Polynomials | Derivatives

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 103 - 120

In this paper, we provide the formulas of general solution for some impulsive differential equations of fractional-order qâˆˆ(1, 2).

Impulsive fractional differential equations | Fractional differential equations | General solution | Impulse | Differential equations

Impulsive fractional differential equations | Fractional differential equations | General solution | Impulse | Differential equations

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 3, pp. 1492 - 1500

We establish the long-time asymptotic formula of solutions to the ( 1 + Î± ) -order fractional differential equation 0 i O t 1 + Î± x + a ( t ) x = 0 , t > 0 ,...

Linear fractional differential equation | Asymptotic integration | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Operators | Solution space | Asymptotic properties | Mathematical analysis | Differential equations | Constrictions | Mathematical models | Derivatives

Linear fractional differential equation | Asymptotic integration | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Operators | Solution space | Asymptotic properties | Mathematical analysis | Differential equations | Constrictions | Mathematical models | Derivatives

Journal Article

12.
Full Text
Stability analysis of higher order nonlinear differential equations in Î²â€“normed spaces

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 03/2019, Volume 42, Issue 4, pp. 1151 - 1166

In this paper, we interrogate different Ulam type stabilities, ie, Î²â€“Ulamâ€“Hyers stability, generalized Î²â€“Ulamâ€“Hyers stability, Î²â€“Ulamâ€“Hyersâ€“Rassias stability,...

Picard operator | Î²â€“Ulamâ€“Hyersâ€“Rassias stability | Lipschitz condition | integrable impulse of fractional type | HYERS-ULAM STABILITY | MATHEMATICS, APPLIED | beta-Ulam-Hyers-Rassias stability | Nonlinear equations | Stability analysis | Mathematical analysis | Differential equations

Picard operator | Î²â€“Ulamâ€“Hyersâ€“Rassias stability | Lipschitz condition | integrable impulse of fractional type | HYERS-ULAM STABILITY | MATHEMATICS, APPLIED | beta-Ulam-Hyers-Rassias stability | Nonlinear equations | Stability analysis | Mathematical analysis | Differential equations

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2019, Volume 362, pp. 172 - 184

This paper presents a spectral Tau method based on MÃ¼ntzâ€“Jacobi basis functions for approximating the solutions of fractional order Volterra...

MÃ¼ntzâ€“Jacobi Tau method | Numerical solvability | Fractional order Volterra integro-differential algebraic equation | Convergence analysis | MATHEMATICS, APPLIED | Muntz-Jacobi Tau method | SPLINE COLLOCATION | SYSTEMS | COLLOCATION METHODS | Methods | Differential equations

MÃ¼ntzâ€“Jacobi Tau method | Numerical solvability | Fractional order Volterra integro-differential algebraic equation | Convergence analysis | MATHEMATICS, APPLIED | Muntz-Jacobi Tau method | SPLINE COLLOCATION | SYSTEMS | COLLOCATION METHODS | Methods | Differential equations

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 10/2018, Volume 115, pp. 362 - 370

â€¢Local and global stability analysis.â€¢Numerical technique for fractional differentiation.â€¢Modelling with Atanganaâ€“Baleanu derivative based on nonlocal and...

Fractional differential equation | Local and global stability | Spatiotemporal oscillations | Numerical simulations | Relative error | Chaotic system | MATHEMATICAL-ANALYSIS | PHYSICS, MULTIDISCIPLINARY | PATTERNS | POWER | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPERATOR | REACTION-DIFFUSION SYSTEMS | NUMERICAL-SIMULATION

Fractional differential equation | Local and global stability | Spatiotemporal oscillations | Numerical simulations | Relative error | Chaotic system | MATHEMATICAL-ANALYSIS | PHYSICS, MULTIDISCIPLINARY | PATTERNS | POWER | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPERATOR | REACTION-DIFFUSION SYSTEMS | NUMERICAL-SIMULATION

Journal Article

Mathematical and Computer Modelling, ISSN 0895-7177, 2009, Volume 50, Issue 3, pp. 386 - 392

In this paper, we introduce fractional-order into a model of HIV infection of CD4 + T-cells. We show that the model established in this paper possesses...

Stability | Differential equation | Numerical solution | Fractional-order | HIV infection | Equilibrium | Predictor-corrector method | CHAOS | MATHEMATICS, APPLIED | DYNAMICS | SYSTEMS

Stability | Differential equation | Numerical solution | Fractional-order | HIV infection | Equilibrium | Predictor-corrector method | CHAOS | MATHEMATICS, APPLIED | DYNAMICS | SYSTEMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2002, Volume 265, Issue 2, pp. 229 - 248

We discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order. The differential operators are...

numerical methods | differential equations | fractional order | Numerical methods | Fractional order | Differential equations | MATHEMATICS | MATHEMATICS, APPLIED | CALCULUS APPROACH | Analysis

numerical methods | differential equations | fractional order | Numerical methods | Fractional order | Differential equations | MATHEMATICS | MATHEMATICS, APPLIED | CALCULUS APPROACH | Analysis

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 12/2017, Volume 122, pp. 66 - 81

In this paper, we define a new set of functions called fractional-order Bernoulli functions (FBFs) to obtain the numerical solution of linear and nonlinear...

Operational matrix | Fractional integro-differential equations | Least square approximation method | Fractional-order Bernoulli functions | Convergence analysis | DELAY SYSTEMS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | INTEGRAL-EQUATIONS | DIFFUSION EQUATION | NUMERICAL-SOLUTION | COLLOCATION METHOD | TAYLOR-SERIES | BLOCK-PULSE FUNCTIONS | LEGENDRE FUNCTIONS | Differential equations

Operational matrix | Fractional integro-differential equations | Least square approximation method | Fractional-order Bernoulli functions | Convergence analysis | DELAY SYSTEMS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | INTEGRAL-EQUATIONS | DIFFUSION EQUATION | NUMERICAL-SOLUTION | COLLOCATION METHOD | TAYLOR-SERIES | BLOCK-PULSE FUNCTIONS | LEGENDRE FUNCTIONS | Differential equations

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2014, Volume 259, pp. 11 - 22

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method...

Multi-term fractional differential equation | Distributed order differential equation | Numeric

Multi-term fractional differential equation | Distributed order differential equation | Numeric