Browsing by Author "Kumar D."

Now showing 1 - 4 of 4
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    A generalized kinetic model of the advection-dispersion process in a sorbing medium
    (2021-01-01) Baleanu D.; Kumar D.; Hristov J.; Vieru D.; Fetecau C.; Ahmed N.; Shah N.A.
    A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu time-fractional derivative is defined along with the associated integral operator. Some properties of the new operators are proved. The new operator is suitable to generate by particularization the known Atangana-Baleanu, Caputo-Fabrizio and Caputo time-fractional derivatives. A generalized mathematical model of the advection-dispersion process with kinetic adsorption is formulated by considering the constitutive equation of the diffusive flux with the new generalized time-fractional derivative. Analytical solutions of the generalized advection-dispersion equation with kinetic adsorption are determined using the Laplace transform method. The solution corresponding to the ordinary model is compared with solutions corresponding to the four models with fractional derivatives.
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    Initial value problem for fractional Volterra integrodifferential pseudo-parabolic equations
    (2021-01-01) Baleanu D.; Kumar D.; Hristov J.; Phuong N.D.; Tuan N.A.; Kumar D.; Tuan N.H.
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    Local generalization of transversality conditions for optimal control problem
    (2019-01-01) Kumar D.; Baleanu D.; Hristov J.; Nieto J.J.; Ozdemir N.; Iskender Eroglu B.B.; Yapişkan D.
    In this paper, we introduce the transversality conditions of optimal control problems formulated with the conformable derivative. Since the optimal control theory is based on variational calculus, the transversality conditions for variational calculus problems are first investigated and then supported by some illustrative examples. Utilizing from these formulations, the transversality conditions for optimal control problems are attained by using the Hamiltonian formalism and Lagrange multiplier technique. To illustrate the obtained results, the dynamical system on which optimal control problem constructed is taken as a diffusion process modeled in terms of the conformable derivative. The optimal control law is achieved by analytically solving the time dependent conformable differential equations occurring from the eigenfunction expansions of the state and the control functions. All figures are plotted using MATLAB.
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    On the initial value problem for fractional Volterra integrodifferential equations with a Caputo-Fabrizio derivative
    (2021-01-01) Baleanu D.; Kumar D.; Hristov J.; Tuan N.H.; Tuan N.A.; O'Regan D.; Tri V.V.
    In this paper, a time-fractional integrodifferential equation with the Caputo-Fabrizio type derivative will be considered. The Banach fixed point theorem is the main tool used to extend the results of a recent paper of Tuan and Zhou [J. Comput. Appl. Math. 375 (2020) 112811]. In the case of a globally Lipschitz source terms, thanks to the Lp - Lq estimate method, we establish global in time well-posed results for mild solution. For the case of locally Lipschitz terms, we present existence and uniqueness results. Also, we show that our solution will blow up at a finite time. Finally, we present some numerical examples to illustrate the regularity and continuation of the solution based on the time variable.