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Periodic Conditions to the Problem Contain $\Psi-$ Hilfer Nonlinear Integro-Fractional Differential Equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 22 مرداد 1405 اصل مقاله (1.32 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.68559.3324 | ||
| نویسندگان | ||
| Baibeen Sadeeq Faris* ؛ Ava Shafeeq Rafeeq | ||
| Department of Mathematics, College of Science, University of Zakho, Zakho, Iraq. | ||
| چکیده | ||
| In this paper, we discuss the $\psi$-Hilfer fractional differential equation of type $\mathfrak{B}$ belonging to $[0, 1]$ and order $1 < \alpha < 2$ involving the $\Psi -$Riemann-Liouville fractional integral of order $0 < \mathfrak{F} < 1$ with periodic boundary conditions. The existence and uniqueness of the solution are proven using Leray-Schauder's and Banach fixed-point theorems. We also analyze the stability of our solutions; Ulam-Hyers and Ulam-Hyers-Rassias theorems are present. The problem with periodic integral boundary conditions is crucial because they provide rich mathematical challenges and help us better understand and optimize systems that exhibit periodic behavior with global constraints. For instance, in optimization, integral constraints represent total resources, such as energy or cost, while periodic integral boundary conditions help optimize cyclical systems, like minimizing energy over repeating cycles. In control theory, they model systems where output must meet total requirements (e.g., fuel consumption) over a period, with periodic conditions capturing the system’s repetitive nature. Finally, an illustrative example is provided to elucidate the theorems presented in this article. | ||
| کلیدواژهها | ||
| $\Psi$-Hilfer fractional derivative؛ existence؛ uniqueness؛ stability؛ nonlinear theorem | ||
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