Application of variational iteration method to fractional hyperbolic partial differential equations.
Applications of certain linear operators in the theory of analytic functions
The object of the present paper is to illustrate the usefulness, in the theory of analytic functions, of various linear operators which are defined in terms of (for example) fractional derivatives and fractional integrals, Hadamard product or convolution, and so on.
Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions
2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15By making use of the fractional differential operator Ω^λz (0 ≤ λ < 1) due to Owa and Srivastava, a new subclass of univalent functions denoted by k−SPλ (0 ≤ k < ∞) is introduced. The class k−SPλ unifies the concepts of k-uniformly convex functions and k-starlike functions. Certain basic properties of k − SPλ such as inclusion theorem, subordination theorem, growth theorem and class preserving transforms are studied.*...
Argument estimates for certain analytic functions associated with the convolution structure.
Asymptotics of integrodifferential models with integrable kernels II.
Asymptotics of integrodifferential models with integrable kernels.
Blow Up Results for Fractional Differential Equations and Systems
Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces
In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order .
Boundary value problems for differential equations with fractional order.
Boundary value problems for differential inclusions with fractional order
In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.
Boundary value problems for Hadamard-Caputo implicit fractional differential inclusions with nonlocal conditions
In this paper, the authors establish sufficient conditions for the existence of solutions to implicit fractional differential inclusions with nonlocal conditions. Both of the cases of convex and nonconvex valued right hand sides are considered.
Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces.
Boundedness properties of fractional integral operators associated to non-doubling measures
The main purpose of this paper is to investigate the behavior of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed power of its radius. This allows, in particular, non-doubling measures. It turns out that this condition is enough to build up a theory that contains the classical results based upon the Lebesgue measure on Euclidean space and their known extensions for doubling...
Calculus of Variations with Classical and Fractional Derivatives
MSC 2010: 49K05, 26A33We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric problems are considered.
Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue
Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15The popular elastic law of Fung that describes the non-linear stress- strain behavior of soft biological tissues is extended into a viscoelastic material model that incorporates fractional derivatives in the sense of Caputo. This one-dimensional material model is then transformed into a three-dimensional constitutive model that is suitable for general analysis. The model is derived in a configuration that differs from the current, or spatial,...
Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative
2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones. Whereas the Riemann-Liouville definition of a fractional derivative is usually employed in mathematical texts and not so frequently in applications, and the Grünwald-Letnikov definition – for numerical approximation of both Caputo and Riemann-Liouville fractional derivatives,...
Cauchy Problem for Differential Equation with Caputo Derivative
The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution...
Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative
2000 Mathematics Subject Classification: 35A15, 44A15, 26A33The paper is devoted to the study of the Cauchy-type problem for the differential equation [...] involving the Riemann-Liouville partial fractional derivative of order α > 0 [...] and the Laplace operator.
Certain Properties of Fractional Calculus Operators Associated with Generalized Mittag-Leffler Function
Mathematics Subject Classification: 26A33, 33E12, 33C20.It has been shown that the fractional integration and differentiation operators transform such functions with power multipliers into the functions of the same form. Some of the results given earlier by Kilbas and Saigo follow as special cases.
Characterization properties for starlike and convex functions involving a class of fractional integral operators