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On fractional derivatives with generalized Mittag-Leffler kernels
(Pushpa Publishing House, 2018) Abdeljawad, Thabet; Baleanu, Dumitru
Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The action of the presented fractional integrals on the Caputo and Riemann type derivatives with three parameter Mittag-Leffler kernels is analyzed. Integration by parts formulas in the sense of Riemann and Caputo are proved and then used to formulate the fractional Euler-Lagrange equations with an illustrative example. Certain nonconstant functions whose fractional derivatives are zero are determined as well.
On the solutions of a fractional boundary value problem
(Scientific Technical Research Council Turkey-Tubitak, 2018) Uğurlu, Ekin; Baleanu, Dumitru; Taş, Kenan
This paper is devoted to showing the existence and uniqueness of solution of a regular second-order nonlinear fractional differential equation subject to the ordinary boundary conditions. The Banach fixed point theorem is used to prove the results.
Symmetry in Applied Continuous Mechanics
(MDPI, 2019) Marin, Marin; Baleanu, Dumitru; Vlase, Sorin
Engineering practice requires the use of structures containing identical components or parts, which are useful from several points of view: less information is needed to describe the system, design is made quicker and easier, components are made faster than a complex assembly, and finally the time to achieve the structure and the cost of manufacturing decreases. Additionally, the subsequent maintenance of the system becomes easier and cheaper. This Special Issue is dedicated to this kind of mechanical structure, describing the properties and methods of analysis of these structures. Discrete or continuous structures in static and dynamic cases are considered. Theoretical models, mathematical methods, and numerical analysis of the systems, such as the finite element method and experimental methods, are expected to be used in the research. Such applications can be used in most engineering fields including machine building, automotive, aerospace, and civil engineering.
The (k, s)-fractional calculus of k-Mittag-Leffler function
(Springer Open, 2017) Nisar, Kottakkaran Sooppy; Rahman, G.; Baleanu, Dumitru; Mubeen, S.; Arshad, Muhammad
In this paper, we introduce the (k, s)-fractional integral and differential operators involving k-Mittag-Leffler function E-k,rho,beta(delta) (z) as its kernel. Also, we establish various properties of these operators. Further, we consider a number of certain consequences of the main results.

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