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.

scholarly journals A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
D. Baleanu ◽  
A. H. Bhrawy ◽  
T. M. Taha
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Laguerre Polynomials ◽  
Collocation Methods ◽  
Half Line ◽  
Caputo Fractional Derivatives ◽  
Polynomial Degree ◽  
Generalized Laguerre Polynomials ◽  
Fractional Differential

This paper deals with modified generalized Laguerre spectral tau and collocation methods for solving linear and nonlinear multiterm fractional differential equations (FDEs) on the half line. A new formula expressing the Caputo fractional derivatives of modified generalized Laguerre polynomials of any degree and for any fractional order in terms of the modified generalized Laguerre polynomials themselves is derived. An efficient direct solver technique is proposed for solving the linear multiterm FDEs with constant coefficients on the half line using a modified generalized Laguerre tau method. The spatial approximation with its Caputo fractional derivatives is based on modified generalized Laguerre polynomialsLi(α,β)(x)withx∈Λ=(0,∞),α>−1, andβ>0, andiis the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre-Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.

scholarly journals Impulsive Problems for Fractional Differential Equations with Nonlocal Boundary Value Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Peiluan Li ◽  
Youlin Shang
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Contraction Mapping Principle ◽  
Impulsive Fractional Differential Equations ◽  
Nonlinear Alternative ◽  
Impulsive Problems ◽  
Fractional Differential

We investigate the nonlocal boundary value problems of impulsive fractional differential equations. By Banach’s contraction mapping principle, Schaefer’s fixed point theorem, and the nonlinear alternative of Leray-Schauder type, some related new existence results are established via a new special hybrid singular type Gronwall inequality. At last, some examples are also given to illustrate the 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.

scholarly journals Impulsive Coupled System of Fractional Differential Equations with Caputo–Katugampola Fuzzy Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Leila Sajedi ◽  
Nasrin Eghbali ◽  
Hassen Aydi
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
The Given ◽  
Stability Results ◽  
Rassias Stability

In this article, we investigate the existence, uniqueness, and different kinds of Ulam–Hyers stability of solutions of an impulsive coupled system of fractional differential equations by using the Caputo–Katugampola fuzzy fractional derivative. We applied the Perov-type fixed point theorem to prove the existence and uniqueness of the proposed system. Furthermore, the Ulam–Hyers–Rassias stability and Ulam–Hyers–Rassias–Mittag-Leffler’s stability results for the given system are discussed.

scholarly journals On a system of Riemann–Liouville fractional differential equations with coupled nonlocal boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Fixed Point Theory ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Point Theory ◽  
Fractional Integrals ◽  
Fractional Differential

AbstractWe investigate the existence of solutions for a system of Riemann–Liouville fractional differential equations with nonlinearities dependent on fractional integrals, subject to coupled nonlocal boundary conditions which contain various fractional derivatives and Riemann–Stieltjes integrals. In the proof of our main results, we use some theorems from the fixed point theory.

scholarly journals Operational shifted hybrid Gegenbauer functions method d for solving multi-term time fractional differential equations

2019 ◽  
Vol 38 (4) ◽  
pp. 97-110
Author(s):  
Nasibeh Seyedi ◽  
Habibollah Saeedi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Fractional Integral ◽  
Good Deal ◽  
Operational Matrices ◽  
Tau Method ◽  
Caputo Fractional Derivatives ◽  
Fractional Differential ◽  
Time Fractional Differential Equations

In this paper, we propose an efficient operational formulation of spectral tau method d for solving multi-term time fractional differential equations with initial-b boundary conditions. The shifted hybrid Gegenbauer functions (SHGFs) operational matrices of Riemann-Liouville fractional integral and Caputo fractional derivatives are presented. By using these operational matrices, the shifted hybrid Gegenbauer functions tau method for both temp oral and spatial discretization are presented, which allow us to introduce an efficient spectral method for solving such problems. Finally, numerical results show good deal with the theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document