Some applications of fractional calculus in engineering.
Some applications of fractional calculus to operator semigroups and functional calculus
We survey some recent results on functional calculus for generators of holomorphic semigroups, which have been obtained using versions of fractional derivation of Riemann-Liouville or Weyl type. Such a calculus allows us to give tight estimates even in concrete L¹ examples.
Some bounding inequalities for the Jacobi and related functions.
Some distortion inequalities associated with the fractional derivatives of analytic and univalent functions.
Some existence results for boundary value problems of fractional differential inclusions with non-separated boundary conditions.
Some Fractional Extensions of the Temperature Field Problem in Oil Strata
This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands are expressed...
Some operational properties of the H-R operator
Some properties of fractional calculus and linear operators associated with certain subclass of multivalent functions.
Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective
Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.Mittag-Leffler functions and their generalizations appear in a large variety of problems in different areas. When we move from total differential equations to fractional equations Mittag-Leffler functions come in naturally. Fractional reaction-diffusion problems in physical sciences and general input-output models in other disciplines are some of the examples in this direction. Some basic properties of Mittag-Leffler functions are...
Some results associated with fractional calculus operators involving Appell hypergeometric function.
Some results for fractional impulsive boundary value problems on infinite intervals
In this paper, we consider a fractional impulsive boundary value problem on infinite intervals. We obtain the existence, uniqueness and computational method of unbounded positive solutions.
Some weighted norm inequalities for a one-sided version of
We study the boundedness of the one-sided operator between the weighted spaces and for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of . For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of from to , where denotes the operator M¯ iterated k times.
Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term.
Stochastic fractional partial differential equations driven by Poisson white noise
We study a stochastic fractional partial differential equations of order driven by a compensated Poisson measure. We prove existence and uniqueness of the solution and we study the regularity of its trajectories.
Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation
Mathematics Subject Classification: 26A33, 76M35, 82B31A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes.
Strict LpSolutions for Nonautonomous Fractional Evolution Equations
MSC 2010: 26A33, 34A08, 34K37
Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivatives
In this article, we present a new method for converting the boundary value problems for impulsive fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some existence results for solutions of a class of boundary value problems for nonlinear impulsive fractional differential systems at resonance case and non-resonance case are established respectively. Our analysis relies on the well known Schauder’s fixed point theorem and coincidence degree theory....
Subordination and superordination for certain analytic functions containing fractional integral.
Sufficient Conditions for One-Sided Operators.
Suggestion from the Past?
Mathematics Subject Classification: 26A33 (main), 35A22, 78A25, 93A30The generalization of the concept of derivative to non-integer values goes back to the beginning of the theory of differential calculus. Nevertheless, its application in physics and engineering remained unexplored up to the last two decades. Recent research motivated the establishment of strategies taking advantage of the Fractional Calculus (FC) in the modeling and control of many phenomena. In fact, many classical engineering...