scholarly journals Study Boundary Problem with Integral condition for Fractional Differential Equations

2020 ◽  
Vol 29 (3) ◽  
pp. 237-245
Author(s):  
Nawal Abdulkader ◽  
Nadia Adnan
Keyword(s):  
Differential Equations ◽  
Boundary Problem ◽  
Fractional Differential Equations ◽  
Integral Condition ◽  
Fractional Differential

scholarly journals Existence of solution for 2-D time-fractional differential equations with a boundary integral condition

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Lotfi Kasmi ◽  
Amara Guerfi ◽  
Said Mesloub
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Integral Condition ◽  
Existence Of Solution ◽  
Boundary Integral ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Time Fractional Differential Equations ◽  
Uniqueness Of A Solution

AbstractIn this article, we prove the existence and uniqueness of a solution for 2-dimensional time-fractional differential equations with classical and integral boundary conditions. We start by writing this problem in the operator form and we choose suitable spaces and norms. Then we establish prior estimates from which we deduce the uniqueness of the strong solution. For the existence of solution for the fractional problem, we prove that the range of the operator generated by the considered problem is dense.

scholarly journals Analysis of some Katugampola fractional differential equations with fractional boundary conditions

2021 ◽  
Vol 18 (6) ◽  
pp. 7269-7279
Author(s):  
Barbara Łupińska ◽  
◽  
Ewa Schmeidel
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Fractional Differential Equations ◽  
Type Inequality ◽  
Fractional Differential ◽  
Fractional Boundary Conditions ◽  
Lyapunov Type Inequality

<abstract><p>In this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary problem. Moreover, we present some examples to demonstrate the effectiveness and applications of the new results.</p></abstract>

Symmetry properties of fractional order transport equations

2012 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
R.K. Gazizov ◽  
A.A. Kasatkin ◽  
S.Yu. Lukashchuk
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Group ◽  
Initial Conditions ◽  
Group Analysis ◽  
Equivalence Transformation ◽  
Point Change ◽  
Infinitesimal Operator ◽  
Symmetry Properties ◽  
Fractional Differential

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.

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

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5217-5239 ◽  
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.

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