Fundamental calculus of the fractional derivative defined with Rabotnov exponential kernel and application to nonlinear dispersive wave model

Before going further with fractional derivative which is constructed by Rabotnov exponential kernel,there exist many questions that are not addressed.In this paper,we try to recapitulate all the fundamental calculus,which we can obtain with this new fractional operator.The problems in this paper are to determine the solutions of the fractional differential equations where the second members are constant functions,polynomial functions,exponential functions,trigonometric functions,or Mittag-Leffler functions.For all the fractional differential equations,the obtained solutions are represented graphically.The Laplace transform of the fractional derivative with Rabotnov exponential kernel is the primary tool in the investigations.Finally,we give the fundamental solution to the nonlinear time-fractional modified Degasperis-Procesi equation by considering the fractional operator with Rabotnov exponential kernel.

夹杂对粉末冶金CT试样蠕变寿命及损伤分布的计算研究

对常载荷下夹杂对粉末冶金材料紧凑拉伸试样蠕变损伤的影响进行数值分析,采用K-R(Kachanov-Rabotnov)模型,主要考虑加载过程中夹杂与基体之间界面的不同失效方式以及夹杂的大小和形状对试样蠕变寿命和蠕变损伤分布的影响。模拟结果表明,当夹杂与基体粘接完好时,试样的最大蠕变损伤在切口部位,而当夹杂从中间破裂形成孔洞或者与基体脱离形成孔洞时,基体的最大蠕变损伤位于夹杂附近,当孔洞存在时会缩短试样的蠕变寿命。在各种失效方式下,含圆形夹杂试样的蠕变寿命比含椭圆形夹杂试样寿命长;对不同的界面失效方式,夹杂的大小和椭圆形夹杂的纵横比对试样的蠕变寿命有不同影响。