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.

Aoun , Abdellatif Ghendir. (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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