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Shivanian, Elyas, Fatahi, Hedayat. (1402). To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition. سامانه مدیریت نشریات علمی, 11(2), 332-344. doi: 10.22034/cmde.2022.51628.2153
Elyas Shivanian; Hedayat Fatahi. "To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition". سامانه مدیریت نشریات علمی, 11, 2, 1402, 332-344. doi: 10.22034/cmde.2022.51628.2153
Shivanian, Elyas, Fatahi, Hedayat. (1402). 'To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition', سامانه مدیریت نشریات علمی, 11(2), pp. 332-344. doi: 10.22034/cmde.2022.51628.2153
Shivanian, Elyas, Fatahi, Hedayat. To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition. سامانه مدیریت نشریات علمی, 1402; 11(2): 332-344. doi: 10.22034/cmde.2022.51628.2153

To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition

Computational Methods for Differential Equations
مقاله 10، دوره 11، شماره 2، تیر 2023، صفحه 332-344    اصل مقاله (346.93 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.51628.2153
نویسندگان
Elyas Shivanian* 1؛ Hedayat Fatahi2
1Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.
2Department of Mathematics, Baneh Branch, Islamic Azad University, Baneh, Iran.
چکیده
In this paper, we prove the existence and uniqueness of the solutions for a non-integer high order boundary value problem which is subject to the Caputo fractional derivative. The boundary condition is a non-local type. Analytically, we introduce the fractional Green’s function. The main principle applied to simulate our results is the Banach contraction fixed point theorem. We deduce this paper by presenting some illustrative examples. Furthermore, it is presented a numerical based semi-analytical technique to approximate the unique solution to the desired order of precision. 
کلیدواژه‌ها
High order fractional differential equation؛ Caputo fractional derivative؛ Boundary value problem؛ Existence and uniqueness؛ Fixed point theorem
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