Browsing by Author "Borisut, Piyachat"

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Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition
(2020) Ahmed, Idris; Kumam, Poom; Abdeljawad, Thabet; Jarad, Fahd; Borisut, Piyachat; Demba, Musa Ahmed; Kumam, Wiyada; 234808; Matematik
The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green’s function of the proposed problems. With the aid of a Green’s function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained. © 2020, The Author(s).
Citation - WoS: 10
Citation - Scopus: 12
Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition
(Springer, 2020) Ahmed, Idris; Kumam, Poom; Abdeljawad, Thabet; Jarad, Fahd; Borisut, Piyachat; Demba, Musa Ahmed; Kumam, Wiyada; 234808; Matematik
The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green's function of the proposed problems. With the aid of a Green's function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained.
Citation - WoS: 51
Citation - Scopus: 62
On Hilfer generalized proportional fractional derivative
(Springer, 2020) Ahmed, Idris; Kumam, Poom; Jarad, Fahd; Borisut, Piyachat; Jirakitpuwapat, Wachirapong; 234808; Matematik
Motivated by the Hilfer and the Hilfer-Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann-Liouville and Caputo generalized proportional fractional derivative. Some important properties of the proposed derivative are presented. Based on the proposed derivative, we consider a nonlinear fractional differential equation with nonlocal initial condition and show that this equation is equivalent to the Volterra integral equation. In addition, the existence and uniqueness of solutions are proven using fixed point theorems. Furthermore, we offer two examples to clarify the results.
Citation - WoS: 27
Citation - Scopus: 23
Stability analysis for boundary value problems with generalized nonlocal condition via Hilfer–Katugampola fractional derivative
(Springer, 2020) Ahmed, Idris; Kumam, Poom; Jarad, Fahd; Borisut, Piyachat; Sitthithakerngkiet, Kanokwan; Ibrahim, Alhassan; 234808; Matematik
In this research, we present the stability analysis of a fractional differential equation of a generalized Liouville-Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boundary condition. Besides, we derive the relation between the proposed problem and the Volterra integral equation. Using the concepts of Banach and Krasnoselskii's fixed point theorems, we investigate the existence and uniqueness of solutions to the proposed problem. Finally, we present two examples to clarify the abstract result.