This paper investigates the existence and uniqueness of solutions for a class of nonlinear $ \Omega $-Caputo fractional differential equations (CFDEs) supplemented with infinite-point boundary conditions. By constructing an appropriate operator framework and employing fixed-point (fp) theorems, including the Banach, the Schaefer, and the Schauder–Tychonoff fp theorems, we establish the existence and uniqueness criteria for the proposed boundary value problem (BVP). The analysis is conducted within suitable Banach spaces, taking into account the properties of the $ \Omega $-Caputo fractional derivative and the nonlocal nature of the boundary conditions. To substantiate the theoretical findings, a concrete example is presented to illustrate the applicability and effectiveness of the main results.
Citation: Özlem Batıt Özen, Aynur Şahin. Nonlinear $ \Omega $-Caputo fractional differential equations with infinite-point boundary conditions[J]. AIMS Mathematics, 2025, 10(9): 20273-20293. doi: 10.3934/math.2025906
This paper investigates the existence and uniqueness of solutions for a class of nonlinear $ \Omega $-Caputo fractional differential equations (CFDEs) supplemented with infinite-point boundary conditions. By constructing an appropriate operator framework and employing fixed-point (fp) theorems, including the Banach, the Schaefer, and the Schauder–Tychonoff fp theorems, we establish the existence and uniqueness criteria for the proposed boundary value problem (BVP). The analysis is conducted within suitable Banach spaces, taking into account the properties of the $ \Omega $-Caputo fractional derivative and the nonlocal nature of the boundary conditions. To substantiate the theoretical findings, a concrete example is presented to illustrate the applicability and effectiveness of the main results.
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Özlem Batıt Özen, Aynur Şahin. Nonlinear $ \Omega $-Caputo fractional differential equations with infinite-point boundary conditions[J]. AIMS Mathematics, 2025, 10(9): 20273-20293. doi: 10.3934/math.2025906
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