Current Issue : October - December Volume : 2019 Issue Number : 4 Articles : 5 Articles
The behavior of the analytical solutions of the fractional differential equation described\nby the fractional order derivative operators is the main subject in many stability problems. In this\npaper, we present a new stability notion of the fractional differential equations with exogenous\ninput. Motivated by the success of the applications of the Mittag-Leffler functions in many areas\nof science and engineering, we present our work here. Applications of Mittag-Leffler functions in\ncertain areas of physical and applied sciences are also very common. During the last two decades, this\nclass of functions has come into prominence after about nine decades of its discovery by a Swedish\nMathematician Mittag-Leffler, due to the vast potential of its applications in solving the problems\nof physical, biological, engineering, and earth sciences, to name just a few. Moreover, we propose\nthe generalized Mittag-Leffler input stability conditions. The left generalized fractional differential\nequation has been used to help create this new notion. We investigate in depth here the Lyapunov\ncharacterizations of the generalized Mittag-Leffler input stability of the fractional differential equation\nwith input....
In this study, we introduce a new modification of fractional reduced differential transform method (m-FRDTM) to find exact\nand approximate solutions for nonhomogeneous linear multiterm time-fractional diffusion equations (MT-TFDEs) of constant\ncoefficients in a bounded domain with suitable initial conditions. Different applications in two and three fractional order terms are\ngiven to illustrate our new modification.The approximate solutions are given in the form of series solutions.The results show that\nthe m-FRDTMforMT-TFDEs is a powerful method and can be generalized to other types of multiterm time-fractional equations....
Multiple-pole soliton solutions to a semidiscretemodified Korteweg-deVries equation are derived by virtue of the Riemann-Hilbert\nproblem with higher-order zeros. A different symmetry condition is introduced to build the nonregular Riemann-Hilbert problem.\nThe simplest multiple-pole soliton solution is presented.The dynamics of the solitons are studied....
The present paper deals with the evaluation of the q -Analogues of Laplece\ntransforms of a product of basic analogues of q 2-special functions. We apply\nthese transforms to three families of q-Bessel functions. Several special cases\nhave been deducted....
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