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 in terms of a convolution of two special functions of Wright’s type.

Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Mathematics Subject Classification: 74D05, 26A33

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30

Existence Results for Fractional Functional Differential Inclusions with Infinite Delay and Applications to Control Theory

Mathematics Subject Classification: 26A33, 34A60, 34K40, 93B05

Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

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

On q-Laplace Transforms of the q-Bessel Functions

Mathematics Subject Classification: 33D15, 44A10, 44A20

Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets

Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60

On q–Analogues of Caputo Derivative and Mittag–Leffler Function

Mathematics Subject Classification: 33D60, 33E12, 26A33

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