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Proceedings of the American Mathematical Society, ISSN 0002-9939, 03/2009, Volume 137, Issue 3, pp. 981 - 989
This paper is devoted to the study of discrete fractional calculus; the particular goal is to define and solve well-defined discrete fractional difference... 
Integers | Method of undetermined coefficients | Difference equations | Real numbers | Constant coefficients | Power rule | Differential equations | Calculus | Mathematical functions | Cauchy problem | Discrete fractional calculus | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 369, Issue 1, pp. 1 - 9
In this paper, we develop some basics of discrete fractional calculus such as Leibniz rule and summation by parts formula. We define simplest discrete... 
Discrete fractional calculus | Calculus of variations | Fractional summation by parts | CANCER GROWTH | MATHEMATICS | MATHEMATICS, APPLIED | GOMPERTZIAN MODEL | CALCULUS | FORMULATION
Journal Article
Mathematical and Computer Modelling, ISSN 0895-7177, 2010, Volume 51, Issue 5, pp. 562 - 571
Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate... 
Nabla discrete fractional calculus | Nabla discrete inequalities | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Journal Article
Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2009, Volume 2009, Issue 3, pp. 1 - 12
Properties of discrete fractional calculus in the sense of a backward difference are introduced and developed. Exponential laws and a product rule are... 
Discrete fractional calculus | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 3, pp. 1591 - 1601
We develop properties of the Laplace Transform in a discrete, fractional calculus setting, giving a precise treatment to convergence along the way. The end... 
Exponential order | Convolution | Taylor monomial | Discrete fractional calculus | Laplace transform | Fractional initial value problem | MATHEMATICS, APPLIED | Calculus | Initial value problems | Mathematical models | Laplace transforms | Mathematical analysis | Convergence
Journal Article
Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2011, Volume 5, Issue 1, pp. 110 - 121
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 14
Journal Article
Computer-Aided Design, ISSN 0010-4485, 09/2019, Volume 114, Issue C, pp. 64 - 72
Fractional partial differential equations (FDEs) are used to describe phenomena that involve a “non-local” or “long-range” interaction of some kind. Accurate... 
Fractional differential equations | Discrete exterior calculus (DEC) | Fractional derivative | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Operators (mathematics) | Differential calculus | Calculus | Partial differential equations | Discretization | MATHEMATICS AND COMPUTING
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 1/2014, Volume 75, Issue 1, pp. 283 - 287
A discrete fractional logistic map is proposed in the left Caputo discrete delta’s sense. The new model holds discrete memory. The bifurcation diagrams are... 
Chaos | Engineering | Vibration, Dynamical Systems, Control | Discrete fractional calculus | Caputo delta difference | Mechanics | Automotive Engineering | Time scale | Mechanical Engineering | SYSTEM | ORDER | MECHANICS | CALCULUS | EQUATIONS | ENGINEERING, MECHANICAL | Bifurcations
Journal Article
Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 10/2013, Volume 7, Issue 2, pp. 343 - 353
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2015, Volume 2015, Issue 1, pp. 1 - 7
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 15
In this paper we prove several fractional quantum integral inequalities for the new q-shifting operator Φ q a ( m ) = q m + ( 1 − q ) a ${_{a}}\Phi_{q}(m) = qm... 
fractional integral inequalities | quantum calculus | 05A30 | 26D10 | Analysis | 26A33 | Mathematics, general | Mathematics | Applications of Mathematics | fractional integral | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | Texts | Operators | Calculus | Integrals | Mathematical analysis | Inequalities
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 6/2015, Volume 80, Issue 4, pp. 1697 - 1703
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2012, Volume 140, Issue 5, pp. 1605 - 1612
In this work we derive a Gronwall type inequality within the discrete fractional setting. Our results constitute generalizations on the inequalities of... 
Differential calculus | Literature | Difference equations | Real numbers | Differential equations | Mathematical inequalities | Calculus | Cauchy problem | Differential variability inequalities | Discrete fractional calculus | Gronwall inequality | Comparison theorem | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENCE | EQUATIONS | comparison theorem
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 01/2016, Volume 82, pp. 38 - 47
Journal Article
International Journal of Modern Physics B, ISSN 0217-9792, 04/2013, Volume 27, Issue 9, pp. 1330005 - 1330032
Journal Article
Thermal Science, ISSN 0354-9836, 2018, Volume 22, Issue Suppl. 1, pp. S203 - S209
In thermal sciences, it is possible to encounter topics such as Bessel beams, Bessel functions or Bessel equations. In this work, we also present new discrete... 
Discrete fractional calculus | Modified Bessel equation | Nabla operator | modified Bessel equation | nabla operator | THERMODYNAMICS | discrete fractional calculus
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2012, Volume 385, Issue 1, pp. 111 - 124
In this paper, we analyze several different types of discrete sequential fractional boundary value problems. Our prototype equation is − Δ μ 1 Δ μ 2 Δ μ 3 y (... 
Boundary value problem | Cone | Discrete fractional calculus | Sequential fractional difference | Positive solution | EXISTENCE | SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | MULTIPLE POSITIVE SOLUTIONS | INITIAL-VALUE PROBLEMS
Journal Article
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