A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

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 of this problem. Two numerical examples are given.

Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.

An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

2000 Mathematics Subject Classification: 42B10, 43A32.

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37

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

The Stein-Weiss Type Inequality for Fractional Integrals, Associated with the Laplace-Bessel Differential Operator

2000 Math. Subject Classification: Primary 42B20, 42B25, 42B35

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

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

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

On a Differential Equation with Left and Right Fractional Derivatives

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