On the Existence and Multiplicity of Solutions for Dirichlet’s problem for Fractional Differential equations

2016 ◽  
Vol 19 (1) ◽  
Author(s):  
Diego Averna ◽  
Stepan Tersian ◽  
Elisabetta Tornatore
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Caputo Fractional Derivatives ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Nonnegative Solutions ◽  
Fractional Differential ◽  
Dirichlet’S Problem

AbstractIn this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.

Infinitely many solutions to boundary value problem for fractional differential equations

2018 ◽  
Vol 21 (6) ◽  
pp. 1585-1597 ◽  
Author(s):  
Diego Averna ◽  
Angela Sciammetta ◽  
Elisabetta Tornatore
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Infinitely Many Solutions ◽  
Caputo Fractional Derivatives ◽  
Fractional Order Differential Equations ◽  
Critical Point Theorems ◽  
Fractional Differential

Abstract Variational methods and critical point theorems are used to discuss existence of infinitely many solutions to boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. An example is given to illustrate our result.

Multiple solutions to boundary value problem for impulsive fractional differential equations

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Stepan Tersian
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

AbstractWe study the multiplicity of solutions for fractional differential equations subject to boundary value conditions and impulses. After introducing the notions of classical and weak solutions, we prove the existence of at least three solutions to the impulsive problem considered.

scholarly journals Existence and Multiplicity of Solutions to a Boundary Value Problem for Impulsive Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Chunyan He ◽  
Yongzhi Liao ◽  
Yongkun Li
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Critical Point ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

We investigate the existence and multiplicity of solutions to a boundary value problem for impulsive differential equations. By using critical point theory, some criteria are obtained to guarantee that the impulsive problem has at least one solution, at least two solutions, and infinitely many solutions. Some examples are given to illustrate the effectiveness of our results.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

scholarly journals A study on multiterm hybrid multi-order fractional boundary value problem coupled with its stability analysis of Ulam–Hyers type

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Nouara ◽  
Abdelkader Amara ◽  
Eva Kaslik ◽  
Sina Etemad ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Boundary Value Problem ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Research Work ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Numerical Examples ◽  
Fractional Derivatives And Integrals ◽  
Fractional Differential

AbstractIn this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results.

scholarly journals EXISTENCE AND STABILITY RESULTS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TWO CAPUTO FRACTIONAL DERIVATIVES

2019 ◽  
pp. 341
Author(s):  
Mohamed Houas ◽  
Mohamed Bezziou
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Contraction Mapping ◽  
Nonlocal Boundary ◽  
Stability Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Stability Results

In this paper, we discuss the existence, uniqueness and stability of solutions for a nonlocal boundary value problem of nonlinear fractional differential equations with two Caputo fractional derivatives. By applying the contraction mapping and O’Regan fixed point theorem, the existence results are obtained. We also derive the Ulam-Hyers stability of solutions. Finally, some examples are given to illustrate our results.

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