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On existence of mild and classical solutions of second order impulsive implicit differential equations

Jain R. S., Reddy B. S., Kadam S. D.

Fasciculi Mathematici

2018

Nr 61

71--81

In this paper, we establish the existence and uniqueness results of mild and classical solutions for impulsive implicit second order differential equations with nonlocal condition by using contraction principle. Furthermore, we give an example to illustrate our results.

On existence of solutions of impulsive nonlinear functional neutral integro-differential equations with nonlocal condition

Jain R. S., Dhakne M. B.

Demonstratio Mathematica

2015

Vol. 48, nr 3

413--423

In the present paper, we investigate the existence, uniqueness and continuous dependence of mild solutions of an impulsive neutral integro-differential equations with nonlocal condition in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results.

Stochastic impulsive pressure calculations for time dependent human hip joint lubrication

Wierzcholski K.

Acta of Bioengineering and Biomechanics

2012

Vol. 14, no. 4

81-100

The present paper is concerned with the calculation of the stochastic unsteady, impulsive pressure distributions and load carrying capacities in human hip joint for unsteady stochastic conditions, various standard deviations and Gaussian probability density function. The total changes of hydrodynamic pressure caused by viscoelastic synovial fluid properties are completely estimated. Calculations are performed in a super thin layer of biological synovial fluid inside the slide hip joint gap limited by a spherical bone head. Using a new unified operator of summation (UOS) method, the numerical topology of pressure calculation for a difference method is applied. From numerical standpoint the proposed method of solving modified hydrodynamic equations reduces this problem to resolving the partial recurrence non-homogeneous equation of second order with variable coefficients.