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    Öğe
    EXISTENCE AND STABILITY RESULTS OF FRACTIONAL DIFFERENTIAL EQUATIONS MITTAG-LEFFLER KERNEL
    (World Scientific Publ Co Pte Ltd, 2024) Abbas, Ahsan; Mehmood, Nayyar; Akgul, Ali; Amacha, Inas; Abdeljawad, Thabet
    This paper presents the following AB-Caputo fractional boundary value problem (ABC)(0)D(alpha)u(sigma) = G(sigma, u(sigma)), sigma is an element of[0, 1] with integral-type boundary conditions u(0) = 0 = u ''(0), gamma u(1) = lambda integral(1)(0) g(1)(kappa)u(kappa)d kappa, of order 2 < alpha <= 3. Schauder and Krasnoselskii's fixed point theorems are used to find existence results. Uniqueness is obtained via the Banach contraction principle. To investigate the stability of a given problem, Hyers-Ulam stability is discussed. An example is provided to validate our results.
  • [ X ]
    Öğe
    Explicit solitary wave structures for the fractional-order Sobolev-type equations and their stability analysis
    (Elsevier, 2024) Shahzad, Tahir; Ahmed, Muhammad Ozair; Baber, Muhammad Zafarullah; Ahmed, Nauman; Akgul, Ali; Abdeljawad, Thabet; Amacha, Inas
    The current research is concerned with solitary wave structures to the time fractional -order Sobolev-type equations. The special types of Sobolev-type equations are under consideration such as the generalized hyperelastic-rod wave (HRW) equation, and Camassa-Holm (CH) equation. These equations occur in several fields, including particularly in quantum field theory, plasma theory, ecology, consolidation of clay and fluid dynamics. The underlying models are investigated analytically by applying two techniques, such as the generalized projective Riccati equation (GPRE) and the modified auxiliary equation (MAE). The gained results are obtained from the different families of solutions such as, including a periodic wave, kink -type wave peakon, a singular wave, and dark solutions. The gained results are denoted as hyperbolic and trigonometric functions. Furthermore, we check that the underlying models are stable using the concept of linearized stability. The propagation behavior of the gained results is displayed in 3D, 2D, and contour visualizations to investigate the influence of various relevant parameters. These results will help the researchers to understand the physical situations.