• Title/Summary/Keyword: right Caputo fractional derivative

Search Result 4, Processing Time 0.018 seconds

Fractional order optimal control for biological model

  • Mohamed Amine Khadimallah;Shabbir Ahmad;Muzamal Hussain;Abdelouahed Tounsi
    • Computers and Concrete
    • /
    • v.34 no.1
    • /
    • pp.63-77
    • /
    • 2024
  • In this research, we considered fractional order optimal control models for cancer, HIV treatment and glucose.These models are based on fractional order differential equations that describe the dynamics underlying the disease.It is formulated in term of left and right Caputo fractional derivative. Pontryagin's Maximum Principle is used as a necessary condition to find the optimal curve for the respective controls over fixed time period. The formulated problems are numerically solved using forward backward sweep method with generalized Euler scheme.

NUMERICAL SOLUTIONS FOR SPACE FRACTIONAL DISPERSION EQUATIONS WITH NONLINEAR SOURCE TERMS

  • Choi, Hong-Won;Chung, Sang-Kwon;Lee, Yoon-Ju
    • Bulletin of the Korean Mathematical Society
    • /
    • v.47 no.6
    • /
    • pp.1225-1234
    • /
    • 2010
  • Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

POLYNOMIALLY DEMICOMPACT OPERATORS AND SPECTRAL THEORY FOR OPERATOR MATRICES INVOLVING DEMICOMPACTNESS CLASSES

  • Brahim, Fatma Ben;Jeribi, Aref;Krichen, Bilel
    • Bulletin of the Korean Mathematical Society
    • /
    • v.55 no.5
    • /
    • pp.1351-1370
    • /
    • 2018
  • In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.