Yazar "Ali, Ghada" seçeneğine göre listele

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    New analysis of fuzzy fractional Langevin differential equations in Caputo's derivative sense
    (AMER INST MATHEMATICAL SCIENCES-AIMS, 2022) Akram, Muhammad; Muhammad, Ghulam; Allahviranloo, Tofigh; Ali, Ghada
    The extraction of analytical solution of uncertain fractional Langevin differential equations involving two independent fractional-order is frequently complex and difficult. As a result, developing a proper and comprehensive technique for the solution of this problem is very essential. In this article, we determine the explicit and analytical fuzzy solution for various classes of the fuzzy fractional Langevin differential equations (FFLDEs) with two independent fractional-orders both in homogeneous and non-homogeneous cases. The potential solution of FFLDEs is also extracted using the fuzzy Laplace transformation technique. Furthermore, the solution of FFLDEs is defined in terms of bivariate and trivariate Mittag-Leffler functions both in the general and special forms. FFLDEs are a new topic having many applications in science and engineering then to grasp the novelty of this work, we connect FFLDEs with RLC electrical circuit to visualize and support the theoretical results.
  • Küçük Resim
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    A solving method for two-dimensional homogeneous system of fuzzy fractional differential equations
    (American Institute of Mathematical Sciences, 2022) Akram, Muhammad; Muhammad, Ghulam; Allahviranloo, Tofigh; Ali, Ghada
    The purpose of this study is to extend and determine the analytical solution of a twodimensional homogeneous system of fuzzy linear fractional differential equations with the Caputo derivative of two independent fractional orders. We extract two possible solutions to the coupled system under the definition of strongly generalized H-differentiability, uncertain initial conditions and fuzzy constraint coefficients. These potential solutions are determined using the fuzzy Laplace transform. Furthermore, we extend the concept of fuzzy fractional calculus in terms of the MittagLeffler function involving triple series. In addition, several important concepts, facts, and relationships are derived and proved as property of boundedness. Finally, to grasp the considered approach, we solve a mathematical model of the diffusion process using proposed techniques to visualize and support theoretical results.