... secondorder **initial** **value** ...firstorder **initial** **value** problem was computed via the combination of collocation method (finite elements) and genetic algo- rithms by the author in ...secondorder ...

7

... boundary **value** **problems** for dynamic equations on time scales were studied in [4] and ...dynamic **initial** **value** **problems** using lower and upper solutions were studied by ...

11

... In this paper, the q-homotopy analysis method is applied to solve linear and nonlinear fractional **initial**-**value** **problems** (fIVPs). The fractional derivatives are described by Caputo’s sense. Exact ...

15

... the **initial** **value** **problems** of fractional diﬀerential equations are discussed and new criteria on local existence and uniqueness of solutions are ...the **problems**, but we also establish ...

17

... the **initial** **value** **problems** of fractional evolution equations are proved under some appropriate conditions by using a fantastic property of the Mittag–Leﬄer ...the **initial** **value** ...

13

... of **initial**-**value** ...of **problems** with several time scales, where one is primarily interested in the long time scale ...for **problems** of sta- bility, fluctuations and confinement in fusion plasma ...

10

... It is a documented fact that mathematical formulation of physical phenomena in many diverse fields such as electrical engineering, control theory, medicine and even in biology often leads to **initial** **value** ...

6

... In this paper, the standard homotopy analysis method was applied to **initial** **value** **problems** of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the ...

16

... In this work, we structure a Feedforward Neural Network (FNN)in order to get the solution of **Initial** **Value** **Problems** (IVPs). The output of the network depends on the trial function, which satisfies ...

12

... Our aim is twofold. First, we propose a natural definition of index for linear nonau- tonomous implicit diﬀerence equations, which is similar to that of linear diﬀerential- algebraic equations. Then we extend this index ...

6

... of **initial** **value** partial differential equations is ...stability **problems** within ideal and resistive magnetohydrodynamics (MHD) are ...advanced **initial** **value** **problems** in fluid ...

21

... impulsive **initial** **value** **problems** for a class of implicit fractional differential equations involving the Caputo fractional derivative of order β ∈ (1, ...

14

... Abstract. In this article, we developed a new numerical approach which is mainly concentrates to solve some complicated **initial** **value** **problems** of ordinary differential equations. The complete ...

6

... Using the discrete Fourier transform and Galerkin-Petrov scheme, we get some results on the solutions and the convergence estimates for periodic pseudodiﬀerential initial value problems.[r] ...

11

... consider **Initial** **Value** **Problems** (IVPs) in ordinary differential equations (ODEs) as an optimization problem, solved by using a meta-heuristic algorithm which is considered as an alternative way to ...

6

... the **problems** to be solved typically are causal, the method is acausal in the sense that the time dependence is calculated by a global mini- mization procedure (the weighted residual formalism) acting on the time ...

20

... In this subsection, we establish some criteria for the global existence, extension, bound- edness, and stabilities of solutions to the local **initial** **value** problem. By Lemmas 2.1 and 2.2, the **initial** ...

14

... **Problems** for which λ has a very large, negative real part are called stiff. Physically they are very stable, but they pose numerical **problems** for ex- plicit methods since the region of stability does not ...

20

... Existence results obtained by Yaker and Koksal are improved for the class of continuous functions. Monotone method coupled with lower and upper solutions is developed for the **initial** **value** problem (1.1) − ...

9

... Working within the framework of the linearized dynamical theory of thermoelasticity, Dafermos [9 J established the existence, uniqueness and asymptotic stability of "generalized solution[r] ...

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