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  1. In this paper, we study a class of initial value problems for a nonlinear implicit fractional differential equation with nonlocal conditions involving the Atangana–Baleanu–Caputo fractional derivative. The app...

    Authors: Abeer S. Alnahdi, Mdi Begum Jeelani, Mohammed S. Abdo, Saeed M. Ali and S. Saleh
    Citation: Boundary Value Problems 2021 2021:104
  2. The objective of the article is to improve the algorithms for the resolution of the spectral discretization of the vorticity–velocity–pressure formulation of the Navier–Stokes problem in two and three domains....

    Authors: Mohamed Abdelwahed, Nejmeddine Chorfi and Henda Ouertani
    Citation: Boundary Value Problems 2021 2021:99
  3. In this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems. We first study the Green function of the Sturm–Liouville d...

    Authors: Zihan Li, Xiao-Bao Shu and Tengyuan Miao
    Citation: Boundary Value Problems 2021 2021:97
  4. Consider nonlinear wave equations in the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. We show blow-up in finite time of solutions and upper bounds of the lifespan of blow-up solutions ...

    Authors: Kimitoshi Tsutaya and Yuta Wakasugi
    Citation: Boundary Value Problems 2021 2021:94
  5. In this paper, by using the energy estimates, the structure of the equations, and the properties of one dimension, we establish the global existence and uniqueness of strong and classical solutions to the init...

    Authors: Menglong Su
    Citation: Boundary Value Problems 2021 2021:92
  6. The Sturm–Liouville equation is among the significant differential equations having many applications, and a lot of researchers have studied it. Up to now, different versions of this equation have been reviewe...

    Authors: Mehdi Shabibi, Akbar Zada, Hashem Parvaneh Masiha and Shahram Rezapour
    Citation: Boundary Value Problems 2021 2021:90
  7. The aim of this paper is to establish some results about the existence of multiple solutions for the following singular semipositone boundary value problem of fourth-order differential systems with parameters:

    Authors: Longfei Lin, Yansheng Liu and Daliang Zhao
    Citation: Boundary Value Problems 2021 2021:79
  8. In this work, we investigate the existence, uniqueness, and stability of fractional differential equation with multi-point integral boundary conditions involving the Caputo fractional derivative. By utilizing ...

    Authors: Mehboob Alam, Akbar Zada, Ioan-Lucian Popa, Alireza Kheiryan, Shahram Rezapour and Mohammed K. A. Kaabar
    Citation: Boundary Value Problems 2021 2021:73
  9. In this paper, we study the effect of Hardy potential on the existence or nonexistence of solutions to the following fractional problem involving a singular nonlinearity:

    http://static-content.springer.com/image/art%3A10.1186%2Fs13661-021-01545-2/13661_2021_1545_Article_Equa.gif ...

    Authors: Masoud Bayrami-Aminlouee, Mahmoud Hesaaraki, Mohamed Karim Hamdani and Nguyen Thanh Chung
    Citation: Boundary Value Problems 2021 2021:68
  10. In this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to...

    Authors: Amar Benkerrouche, Mohammed Said Souid, Kanokwan Sitthithakerngkiet and Ali Hakem
    Citation: Boundary Value Problems 2021 2021:64

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