Quasi-Interpolant Operators and the Solution of Fractional Differential Problems

In the paper some features of applying Lie group analysis methods to fractional differential equations are considered. The problem related to point change of variables in the fractional differentiation operator is discussed and some general form of transformation that conserves the form of Riemann-Liouville fractional operator is obtained. The prolongation formula for extending an infinitesimal operator of a group to fractional derivative with respect to arbitrary function is presented. Provided simple example illustrates the necessity of considering both local and non-local symmetries for fractional differential equations in particular cases including the initial conditions. The equivalence transformation forms for some fractional differential equations are discussed and results of group classification of the wave-diffusion equation are presented. Some examples of constructing particular exact solutions of fractional transport equation are given, based on the Lie group methods and the method of invariant subspaces.

Download Full-text

Solving Fuzzy Fractional Boundary Value Problems Using Fractional Differential Transform Method

Journal of Al-Nahrain University-Science ◽

10.22401/jnus.16.4.28 ◽

2013 ◽

Vol 16 (4) ◽

pp. 225-232 ◽

Cited By ~ 1

Author(s):

Osama H. Mohammed ◽

Salam A. Ahmed

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Differential Transform Method ◽

Transform Method ◽

Differential Transform ◽

Fractional Differential ◽

Fractional Boundary Value Problems

Download Full-text

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽

10.2298/fil1702451b ◽

2017 ◽

Vol 31 (2) ◽

pp. 451-460 ◽

Cited By ~ 1

Author(s):

Mohammed Belmekki ◽

Kheira Mekhalfi

Keyword(s):

Differential Equations ◽

Measure Of Noncompactness ◽

Mild Solutions ◽

Functional Differential Equations ◽

Kuratowski Measure Of Noncompactness ◽

State Dependent ◽

State Dependent Delay ◽

Liouville Fractional Derivative ◽

Fractional Differential ◽

Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

Download Full-text

Caputo fractional differential equations with non-instantaneous impulses and strict stability by Lyapunov functions

Filomat ◽

10.2298/fil1716217a ◽

2017 ◽

Vol 31 (16) ◽

pp. 5217-5239 ◽

Cited By ~ 5

Author(s):

Ravi Agarwal ◽

Snehana Hristova ◽

Donal O’Regan

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Lyapunov Functions ◽

Sufficient Conditions ◽

Time Intervals ◽

Dini Derivative ◽

Comparison Results ◽

Strict Stability ◽

Caputo Fractional Differential Equations ◽

Fractional Differential

In this paper the statement of initial value problems for fractional differential equations with noninstantaneous impulses is given. These equations are adequate models for phenomena that are characterized by impulsive actions starting at arbitrary fixed points and remaining active on finite time intervals. Strict stability properties of fractional differential equations with non-instantaneous impulses by the Lyapunov approach is studied. An appropriate definition (based on the Caputo fractional Dini derivative of a function) for the derivative of Lyapunov functions among the Caputo fractional differential equations with non-instantaneous impulses is presented. Comparison results using this definition and scalar fractional differential equations with non-instantaneous impulses are presented and sufficient conditions for strict stability and uniform strict stability are given. Examples are given to illustrate the theory.

Download Full-text