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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
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
Book
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
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
Book
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
eBook
Applied Mathematics and Computation, ISSN 0096-3003, 11/2018, Volume 336, pp. 433 - 453
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
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 04/2013, Volume 37, Issue 7, pp. 5498 - 5510
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 q∈(1, 2). 
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 + α ) -order fractional differential equation 0 i O t 1 + α 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
Journal Article
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, β–Ulam–Hyers stability, generalized β–Ulam–Hyers stability, β–Ulam–Hyers–Rassias stability,... 
Picard operator | β–Ulam–Hyers–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 Müntz–Jacobi basis functions for approximating the solutions of fractional order Volterra... 
Müntz–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
•Local and global stability analysis.•Numerical technique for fractional differentiation.•Modelling with Atangana–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
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
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
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