On a new class of abstract impulsive differential equations

By E. Hernández, Donal O'Regan. 2012

462 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9e0d10e3ee4f46a32398d72ce47b4d8e9efbcab0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Akbar Zada
2. Jinrong Wang
3. Wajid Ali
4. Dwijendra Narain Pandey
5. Xuezhu Li
6. Dhirendra Bahuguna
7. Rajesh Dhayal
8. Muslim Malik

In Control and Systems Engineering

1. Rajesh Dhayal
2. Muslim Malik
3. Syed Abbas
4. S. Farina
5. Dwijendra Narain Pandey
6. Jinrong Wang
7. Dhirendra Bahuguna
8. Akbar Zada

In Numerical Analysis

1. Wajid Ali
2. Rajesh Dhayal
3. Muslim Malik
4. Syed Abbas
5. S. Farina
6. Xuezhu Li
7. Jinrong Wang
8. Dhirendra Bahuguna

Citations in the corpus

• Hyers–Ulam stability of nonlinear differential equations with fractional integrable impulses (2017, methodology): “discussed Ulam’s type stability for the class of differential equations introduced in [34].”
• Approximate and trajectory controllability of fractional stochastic differential equation with non‐instantaneous impulses and Poisson jumps (2020, background): “For more details on non-instantaneous impulses, one can see [13-17] and the references cited therein.”
• Existence and Hyers‐Ulam stability of fractional nonlinear impulsive switched coupled evolution equations (2018, unknown): “For any (u, v) ∈ 𝔅r, we have||ϝ(𝑝, q) + G(𝑝, q)||PC ≤ ||ϝ(𝑝, q)||PC + ||G(𝑝, q)||PC = ||ϝ1𝑝||PC + ||ϝ2q||PC + ||G1(𝑝, q)||PC + ||G2(𝑝, q)||PC. (9) From (7), we get |ϝ1𝑝(t)| ≤ |||||𝑝0 − 𝜙(𝑝) + m∑ k=1 Ik(𝑝(tk)) + 1 Γ(𝜎) m∑ k=1 ∫ tk tk−1 (tk − 𝜂)𝜎−11(𝜂)𝑝(𝜂)d𝜂 ||||| + ||||| 1Γ(𝜎) ∫ ”
• On a new class of abstract impulsive functional differential equations of fractional order (2014, background): “…equations as these equations provide a natural frame ∗Corresponding author Email addresses: prdipk@gmail.com (Pradeep Kumar), dwij.iitk@gmail.com (Dwijendra N. Pandey), dhiren@iitk.ac.in (D. Bahuguna) Received 2013-04-30 work for mathematical modelling of many real world phenomena, namely in the…”
• Stability Analysis for a General Class of Non-instantaneous Impulsive Differential Equations (2017, unknown): “Motivated by Hernández and O’Regan [2], Wang and Fečkan [16,17] extended the study to a new generalized class of differential equations with non-instantaneous impulses, which depend on the previous state.”
• Periodic BVP for integer/fractional order nonlinear differential equations with non-instantaneous impulses (2014, background): “It is remarkable that Hernández and O’Regan [2] and Pierri et al.”