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.

The method of upper and lower solutions for integral boundary value problem of semilinear fractional differential equations with non-instantaneous impulses

2020 ◽  
Vol 70 (3) ◽  
pp. 625-640 ◽  
Author(s):  
Mengrui Xu ◽  
Shurong Sun ◽  
Zhenlai Han
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Existence Results ◽  
Three Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Fractional Differential

AbstractIn this paper, we investigate a class of semilinear fractional differential equations with non-instantaneous impulses and integral boundary value conditions. By the method of upper and lower solutions combined with Amann three-solution theorem, existence results of at least three solutions are obtained.

Existence of solutions to boundary value problem for impulsive fractional differential equations

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Gabriele Bonanno ◽  
Rosana Rodríguez-López ◽  
Stepan Tersian
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Existence Results ◽  
Three Solutions ◽  
Fractional Order Differential Equations ◽  
Impulsive Fractional Differential Equations ◽  
Impulsive Boundary Value Problem ◽  
Fractional Differential

AbstractIn this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fractional order differential equations. The notions of classical and weak solutions are introduced. Then, existence results of at least one and three solutions are proved.

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.

Weak Solutions for Fractional Differential Equations via Henstock–Kurzweil–Pettis Integrals

2020 ◽  
Vol 21 (2) ◽  
pp. 135-145 ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Measure Of Noncompactness ◽  
Pettis Integral ◽  
Existence Of Weak Solutions ◽  
Fractional Differential

AbstractIn this paper, we used Henstock–Kurzweil–Pettis integral instead of classical integrals. Using fixed point theorem and weak measure of noncompactness, we study the existence of weak solutions of boundary value problem for fractional integro-differential equations in Banach spaces. Our results generalize some known results. Finally, an example is given to demonstrate the feasibility of our conclusions.

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