Controllability of neutral impulsive fractional differential equations with Atangana-Baleanu-Caputo derivatives

2021 ◽  
Vol 150 ◽  
pp. 111153
Author(s):  
Pallavi Bedi ◽  
Anoop Kumar ◽  
Aziz Khan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Caputo Derivatives ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Naveed Ahmad ◽  
Zeeshan Ali ◽  
Kamal Shah ◽  
Akbar Zada ◽  
Ghaus ur Rahman
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Nonlocal Boundary ◽  
Dynamical Problem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We study the existence, uniqueness, and various kinds of Ulam–Hyers stability of the solutions to a nonlinear implicit type dynamical problem of impulsive fractional differential equations with nonlocal boundary conditions involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii’s fixed point theorem. For stability, we utilized classical functional analysis. Also, an example is given to demonstrate our main theoretical results.

Periodic impulsive fractional differential equations

2017 ◽  
Vol 8 (1) ◽  
pp. 482-496 ◽  
Author(s):  
Michal Fečkan ◽  
Jin Rong Wang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Fractional Differential Equations ◽  
Periodic Boundary ◽  
Lorenz System ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Existence Of Periodic Solutions ◽  
Lower Limits ◽  
Stability Results

Abstract This paper deals with the existence of periodic solutions of fractional differential equations with periodic impulses. The first part of the paper is devoted to the uniqueness, existence and asymptotic stability results for periodic solutions of impulsive fractional differential equations with varying lower limits for standard nonlinear cases as well as for cases of weak nonlinearities, equidistant and periodically shifted impulses. We also apply our result to an impulsive fractional Lorenz system. The second part extends the study to periodic impulsive fractional differential equations with fixed lower limit. We show that in general, there are no solutions with long periodic boundary value conditions for the case of bounded nonlinearities.

scholarly journals Multiple Solution Results for Perturbed Fractional Differential Equations with Impulses

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Peiluan Li ◽  
Liang Xu ◽  
Peiyu Li ◽  
Hui Wang
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Morse Theory ◽  
Multiple Solution ◽  
Classical Solutions ◽  
Linking Theorem ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

The multiplicity of classical solutions for impulsive fractional differential equations has been studied by many scholars. Using Morse theory, Brezis and Nirenberg’s Linking Theorem, and Clark theorem, we aim to solve this kind of problems. By this way, we obtain the existence of at least three classical solutions and k distinct pairs of classical solutions. Finally, an example is presented to illustrate the feasibility of the main results in this paper.

A variational approach for boundary value problems for impulsive fractional differential equations

2018 ◽  
Vol 21 (6) ◽  
pp. 1565-1584 ◽  
Author(s):  
Ghasem A. Afrouzi ◽  
Armin Hadjian
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Classical Solutions ◽  
Oscillatory Behaviour ◽  
Impulsive Fractional Differential Equations ◽  
Distinct Sequence ◽  
Fractional Differential ◽  
Critical Point Result

Abstract By using an abstract critical point result for differentiable and parametric functionals due to B. Ricceri, we establish the existence of infinitely many classical solutions for fractional differential equations subject to boundary value conditions and impulses. More precisely, we determine some intervals of parameters such that the treated problems admit either an unbounded sequence of solutions, provided that the nonlinearity has a suitable oscillatory behaviour at infinity, or a pairwise distinct sequence of solutions that strongly converges to zero if a similar behaviour occurs at zero. No symmetric condition on the nonlinear term is assumed. Two examples are then given.

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