Existence of mild solution for evolution equation with Hilfer fractional derivative

By Haibo Gu, Juan Trujillo. Applied Mathematics and Computation, 2015

380 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/db1365b886acfb897e120e706dac0bb74c6dff43

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. V. Vijayakumar
2. R. Udhayakumar
3. Chokkalingam Ravichandran
4. E. Capelas de Oliveira
5. K. Kavitha
6. J. Sousa
7. J. Vanterler
8. Lishan Liu

In Control and Systems Engineering

1. V. Vijayakumar
2. R. Udhayakumar
3. Chokkalingam Ravichandran
4. K. Kavitha
5. Min Yang
6. R. Subashini
7. J. Sousa
8. F. G. Rodrigues

In Modeling and Simulation

1. V. Vijayakumar
2. R. Udhayakumar
3. Chokkalingam Ravichandran
4. E. Capelas de Oliveira
5. K. Kavitha
6. J. Sousa
7. J. Vanterler
8. Danilo C. Sousa

Citations in the corpus

• Results on controllability of Hilfer fractional differential equations with infinite delay via measures of noncompactness (2021, background): “Inspired by this work, recently, many researchers show great interest based on this topic, and the readers can refer to previous studies [18-22].”
• Existence results of Hilfer integro-differential equations with fractional order (2020, methodology): “4.[10] Suppose ν > 0, a nonnegative function a(ω) is locally integrable on 0 ≤ ω ≤ (T ≤ +∞) and g(ω) is nonnegative, increasing continuous and characterized on 0 ≤ ω < T, g(ω) ≤ k (constant), and u(ω) is locally integrable on”
• Approximate controllability of noninstantaneous impulsive Hilfer fractional integrodifferential equations with fractional Brownian motion (2020, background): “2 (see [32]) The operator Sν,μ and Pμ have the following properties.”
• Approximate controllability of Hilfer fractional differential inclusions with nonlocal conditions (2017, background): “Proof We can refer to [34] and [36]; here, we omit it.”
• Existence of mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions (2017, background): “1 in [9], we can easily get that F1 : B → B is continuous.”
• Ulam–Hyers–Rassias Stability for a Class of Fractional Integro-Differential Equations (2018, background): “tinues to expand [3, 4, 5, 6, 7]. On the other hand, there was considerable growth in the study of the existence and uniqueness of solutions of fractional differential equations and integral equations [14, 17, 18, 19, 20, 21, 22, 23]. In fact, it is possible to note that researches involving the exis”
• Stability of the fractional Volterra integro‐differential equation by means of ψ‐Hilfer operator (2018, methodology): “We also mention some recent papers by Katugampola,5 Almeida,6 and Sousa and Oliveira.7,8 Fractional differential equations have already proved to be valuable tools in the modeling of several physical phenomena, because their solutions, in general, allows a better evaluation of the results in several”