Volume 33, Issue 4
Existence of Solutions for Nonlocal Boundary Value Problem of Fractional Differential Equations on the Infinite Interval

Abdellatif Ghendir Aoun

Ann. Appl. Math., 33 (2017), pp. 340-352.

Published online: 2022-06

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  • Abstract

In this paper, we study a fractional differential equation $$^cD^α _{0+} u(t) + f(t, u(t)) = 0, \ t ∈ (0, +∞)$$ satisfying the boundary conditions: $$u′(0)=0,\ \lim\limits_{t→+∞} \ ^cD^{α−1}_{0+} u(t) = g(u),$$ where $1<α\leq 2,$ $^cD^α_{0+}$ is the standard Caputo fractional derivative of order $α.$ The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O’Regan. Under a compactness criterion, the existence of solutions is established.

  • AMS Subject Headings

34A08, 34B40

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COPYRIGHT: © Global Science Press

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@Article{AAM-33-340, author = {Aoun , Abdellatif Ghendir}, title = {Existence of Solutions for Nonlocal Boundary Value Problem of Fractional Differential Equations on the Infinite Interval}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {33}, number = {4}, pages = {340--352}, abstract = {

In this paper, we study a fractional differential equation $$^cD^α _{0+} u(t) + f(t, u(t)) = 0, \ t ∈ (0, +∞)$$ satisfying the boundary conditions: $$u′(0)=0,\ \lim\limits_{t→+∞} \ ^cD^{α−1}_{0+} u(t) = g(u),$$ where $1<α\leq 2,$ $^cD^α_{0+}$ is the standard Caputo fractional derivative of order $α.$ The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O’Regan. Under a compactness criterion, the existence of solutions is established.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20615.html} }
TY - JOUR T1 - Existence of Solutions for Nonlocal Boundary Value Problem of Fractional Differential Equations on the Infinite Interval AU - Aoun , Abdellatif Ghendir JO - Annals of Applied Mathematics VL - 4 SP - 340 EP - 352 PY - 2022 DA - 2022/06 SN - 33 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/20615.html KW - boundary value problem, fractional differential equation, infinite interval, nonlocal condition, fixed point theorem. AB -

In this paper, we study a fractional differential equation $$^cD^α _{0+} u(t) + f(t, u(t)) = 0, \ t ∈ (0, +∞)$$ satisfying the boundary conditions: $$u′(0)=0,\ \lim\limits_{t→+∞} \ ^cD^{α−1}_{0+} u(t) = g(u),$$ where $1<α\leq 2,$ $^cD^α_{0+}$ is the standard Caputo fractional derivative of order $α.$ The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O’Regan. Under a compactness criterion, the existence of solutions is established.

Abdellatif Ghendir Aoun. (2022). Existence of Solutions for Nonlocal Boundary Value Problem of Fractional Differential Equations on the Infinite Interval. Annals of Applied Mathematics. 33 (4). 340-352. doi:
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