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Browsing by Author "Asad, J."

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    Citation - Scopus: 1
    A Fractional Lagrangian Approach for Two Masses With Linear and Cubic Nonlinear Stiffness
    (Institute of Electrical and Electronics Engineers Inc., 2023) Baleanu, D.; Jajarmi, A.; Wannan, R.; Asad, J.; Defterli, O.; 31401; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    In this manuscript, the fractional dynamics of the two-mass spring system with two kinds of stiffness, namely linear and strongly nonlinear, are investigated. The corresponding fractional Euler-Lagrange equations of the system are derived being a system of two-coupled fractional differential equations with strong cubic nonlinear term. The numerical results of the system are obtained using Euler's approximation method and simulated with respect to the different values of the model parameters as mass, stiffness and order of the fractional derivative in use. The interpretation of the approximate results of the so-called generalized two-mass spring system is discussed via the fractional order. © 2023 IEEE.
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    Citation - WoS: 115
    Citation - Scopus: 129
    Novel Fractional-Order Lagrangian To Describe Motion of Beam on Nanowire
    (Polish Acad Sciences inst Physics, 2021) Godwe, E.; Erturk, V. S.; Baleanu, D.; Kumar, P.; Asad, J.; Jajarmi, A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    Our aim in this research is to investigate the motion of a beam on an internally bent nanowire by using the fractional calculus theory. To this end, we first formulate the classical Lagrangian which is followed by the classical Euler-Lagrange equation. Then, after introducing the generalized fractional Lagrangian, the fractional Euler-Lagrange equation is provided for the motion of the considered beam on the nanowire. An efficient numerical scheme is introduced for implementation and the simulation results are reported for different fractional-order values and various initial settings. These results indicate that the fractional responses approach the classical ones as the fractional order goes to unity. In addition, the fractional Euler-Lagrange equation provides a flexible model possessing more information than the classical description the fact that leads to a considerably better evaluation of the hidden features of the real system under investigation.