A recent development in differential equations with variable coefficients by means of fractional operators has been a method for obtaining an exact solution infinite series involving nested integral operators. This representation is constructive but difficult to calculate practice. Here, we show new the function, as convergent single integrals, which computationally simpler and believe will qui...

In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liou...

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of VolterraFredholm type differential equations with nonlocal conditions in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques. MSC: 34K37 • 34A08 • 47H10

We investigate a class of N = 4 quiver Chern-Simons theories and their gravity duals. We define the group of fractional D3-brane charges in a type IIB brane setup with taking account of D3-brane creation due to Hanany-Witten effect, and confirm that it agrees with the 3-cycle homology of the dual geometry, which describes the charges of fractional M2-branes, M5-branes wrapped on 3-cycles. The r...

This paper presents an approach to texture image segmentation using a family of fractional discrimination functions. In contrast to the conventional methods, the proposed functions provide uniform treatment of the existing functions and operators for selective feature extraction. The effectiveness of fractional discrimination functions for texture feature detection is demonstrated in the presen...

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of Volterra-Fredholm type differential equations with impulses in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques. ifx

Abstract. Based on the fractional q–integral with the parametric lower limit of integration, we define fractional q–derivative of Riemann–Liouville and Caputo type. The properties are studied separately as well as relations between them. Also, we discuss properties of compositions of these operators. Mathematics Subject Classification: 33D60, 26A33 .

If φ is an analytic function mapping the unit disk D into itself, the composition operator Cφ is the operator on H 2 given by Cφf = f ◦φ. The structure of the composition operator Cφ is usually complex, even if the function φ is fairly simple. In this paper, we consider composition operators whose symbol φ is a linear fractional transformation mapping the disk into itself. That is, we will assu...

We describe two models of flow in porous media including nonlocal (longrange) diffusion effects. The first model is based on Darcy’s law and the pressure is related to the density by an inverse fractional Laplacian operator. We prove existence of solutions that propagate with finite speed. The model has the very interesting property that mass preserving self-similar solutions can be found by so...