Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group

2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Mathematics Subject Classification: 26A33, 34A37.

Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Mathematics Subject Classification: 26A33, 76M35, 82B31

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63

Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

Mathematics Subject Classification: 45G10, 45M99, 47H09

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

On a Differential Equation with Left and Right Fractional Derivatives

Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05

Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations

Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10

Microstructure-based inherent anisotropy of asphalt mixtures

Asphalt mixtures have been demonstrated to be anisotropic materials in both laboratory and field tests. The anisotropy of asphalt mixtures consists of inherent anisotropy and stress-induced anisotropy. In previous work, the inherent anisotropy of asphalt mixtures was quantified by using only the inclination angles of the coarse aggregate particles in the asphalt mixtures. However, the inclination of fine aggregates also has a contribution to the inherent anisotropy. Moreover, the contribution to the inherent anisotropy of each aggregate may not be the same as in the previous work but will depend on the size, orientation, and sphericity of the aggregate particle. This paper quantifies the internal microstructure of the aggregates in asphalt mixtures by using an aggregate-related geometric parameter, the vector magnitude. The original formulation of the vector magnitude, which addresses only the orientation of coarse aggregates, is modified to account for not only the coarse aggregate orientation, but also the size, orientation, and sphericity of coarse and fine aggregates. This formulation is applied to cylindrical lab-mixed lab-compacted asphalt mixture specimens varying in asphalt binder type, air void content, and aging period. The vertical modulus and the horizontal modulus are also measured by using nondestructive tests. A relationship between the modified vector magnitude and the modulus ratio of the vertical modulus to the horizontal modulus is developed to quantify the influence of the inherent microstructure of the aggregates on the anisotropy of the mixtures. The modulus ratio is found to depend solely on the aggregate characteristics including the inclination angle, size, and sphericity, and it is independent of the asphalt binder type, air void content, and aging period. The inclination angle, itself, proves to be insufficient to quantify the inherent anisotropy of the asphalt mixtures. © 2011 American Society of Civil Engineers.

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05

Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,

Generalized Fractional Evolution Equation

2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20

On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions

Mathematics Subject Classification: 33D60, 33D90, 26A33

Design of Fractional Order Digital Differentiators and Integrators Using Indirect Discretization

Mathematics Subject Classification: 26A33, 93B51, 93C95