Yazar "Zaky, M. A." seçeneğine göre listele

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    Öğe
    Efficient spectral collocation method for nonlinear systems of fractional pantograph delay differential equations
    (Amer Inst Mathematical Sciences-Aims, 2024) Zaky, M. A.; Babatin, M.; Hammad, M.; Akgul, A.; Hendy, A. S.
    Caputo-Hadamard-type fractional calculus involves the logarithmic function of an arbitrary exponent as its convolutional kernel, which causes challenges in numerical approximations. In this paper, we construct and analyze a spectral collocation approach using mapped Jacobi functions as basis functions and construct an efficient algorithm to solve systems of fractional pantograph delay differential equations involving Caputo-Hadamard fractional derivatives. What we study is the error estimates of the derived method. In addition, we tabulate numerical results to support our theoretical analysis.
  • [ X ]
    Öğe
    NUMERICAL RECONSTRUCTION OF A SPACE-DEPENDENT SOURCE TERM FOR MULTIDIMENSIONAL SPACE-TIME FRACTIONAL DIFFUSION EQUATIONS
    (Editura Acad Romane, 2023) Sidi, H. ould; Zaky, M. A.; EL Waled, K.; Akgul, A.; Hendy, A. S.
    In this paper, we consider the problem of identifying the unknown source function in the time-space fractional diffusion equation from the final obser-vation data. An implicit difference technique is proposed in conjunction with the matrix transfer scheme for approximating the solution of the direct problem. The challenge pertains to an inverse scenario encompassing a nonlocal ill-posed operator. The problem under investigation is formulated as a regularized optimization problem with a least-squares cost function minimization objective. An approximation for the source function is obtained using an iterative non-stationary Tikhonov regularization approach. Three numerical examples are reported to verify the efficiency of the pro-posed schemes.