Abstract
Solutions to fractional differential equations is an emerging part of current research, since such equations appear in different applied fields. A study of existence, uniqueness, and stability of solutions to a coupled system of fractional differential equations with non-separated boundary conditions is the main target of this paper. The existence and uniqueness results are obtained by employing the Leray–Schauder fixed point theorem and the Banach contraction principle. Additionally, we examine different types of stabilities in the sense of Ulam–Hyers such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability. To prove the effectiveness of our main results, we study a few interesting examples.
Highlights
In the last few decades, the theory of fractional differential equations (FDEs) has performed a significant role in a new branch of applied mathematics
We refer the reader to a series of papers [1, 5, 12, 15, 16, 19, 28, 31, 33,34,35, 40] for the theoretical works on coupled systems of FDEs and classical differential equations
When Hyers [13] and Rassias [24] generalized this stability to Banach spaces, a number of mathematicians spread the idea of stability to different classes of differential
Summary
In the last few decades, the theory of fractional differential equations (FDEs) has performed a significant role in a new branch of applied mathematics. Li et al [18] investigated the existence and uniqueness of solutions to the following FDEs system with non-separated boundary conditions: cDαx(t) = f t, x(t) , t ∈ [0, T], 1 < α ≤ 2, T > 0, a1x(0) + b1x(T) = c1, a2 cDγ x(0) + b2 cDγ x(T) = c2, 0 < γ < 1, where f ∈ ([0, T] × R), cDα represents the Caputo fractional derivative of order α and ai, bi, ci, for i = 1, 2, are real constants with a1 + b1 = 0 and b2 = 0. Rao and Alesemi [23] investigated the existence and uniqueness of solutions for a coupled system of fractional differential equations with fractional non-separated coupled boundary conditions.
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