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Existence and uniqueness of solutions for multi-order fractional differential equations with integral boundary conditions.
- Source :
- Boundary Value Problems; 1/2/2024, Vol. 2024 Issue 1, p1-14, 14p
- Publication Year :
- 2024
-
Abstract
- In this paper, we consider the existence and uniqueness of solutions for the following nonlinear multi-order fractional differential equation with integral boundary conditions { (C D 0 + α u) (t) + ∑ i = 1 m λ i (t) (C D 0 + α i u) (t) + ∑ j = 1 n μ j (t) (C D 0 + β j u) (t) + ∑ k = 1 p ξ k (t) (C D 0 + γ k u) (t) + ∑ l = 1 q ω l (t) (C D 0 + δ l u) (t) + σ (t) u (t) + f (t , u (t)) = 0 , t ∈ [ 0 , 1 ] , u ″ (0) = u ‴ (0) = 0 , u ′ (0) = η 1 ∫ 0 1 u (s) d s , u (1) = η 2 ∫ 0 1 u (s) d s , where 0 < δ 1 < δ 2 < ⋯ < δ q < 1 < γ 1 < γ 2 < ⋯ < γ p < 2 < β 1 < β 2 < ⋯ < β n < 3 < α 1 < α 2 < ⋯ < α m < α < 4 and η 1 + 2 (1 − η 2) ≠ 0 . Using a fixed point theorem and Banach contractive mapping principle, we obtain some existence and uniqueness results. [ABSTRACT FROM AUTHOR]
- Subjects :
- BOUNDARY value problems
FRACTIONAL differential equations
MATHEMATICAL mappings
Subjects
Details
- Language :
- English
- ISSN :
- 16872762
- Volume :
- 2024
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Boundary Value Problems
- Publication Type :
- Academic Journal
- Accession number :
- 174558876
- Full Text :
- https://doi.org/10.1186/s13661-023-01804-4