# General forms of elastic-plastic matching equations for mode-III cracks near crack line

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The one-dimensional fractional diffusion equation is studied systematically using the non-polynomial spline method. The Caputo fractional derivative is used for formulation. An example is solved to assess the accuracy of the method. The numerical results are obtained for different values (n) of...

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In this paper, we implemented a direct algebraic method for the complex solutions of the fifth order Korteweg-de Vries (KdV) equation and (3+1) dimensional Burgers equation. By using this scheme, we found several complex solutions of the three fifth order KdV equations and (3+1) dimensional...

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This paper continues the investigation of solvability of product-type systems of difference equations, by studying the following system with two variables: zn = Î±zan-1 Ï‰ bn-2, Ï‰n = Î² Ï‰ cn-3 zdn-2, n âˆˆ N0, where a, b, c, d âˆˆ Z, Î±, Î² âˆˆ C\ {0}, Ï‰-3, Ï‰...

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The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist...

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It is known that there exists a class of methods for solving integral equations with variable boundary. One of them is the most popular methods of quadratures. This method is clarified and modified by many scientists. Here, to numerically solving Volterra integral equations the hybrid method is...

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Numerous research works are devoted to study Cauchy mixed problem for model heat equations because of its theoretical and practical importance. Among them we can notice monographers Vladimirov (1988), Ladyzhenskaya (1973), and Tikhonov and Samarskyi (1980) which demonstrate main research...

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We establish necessary and sufficient conditions for the Fredholm property of a planar problem with shift and conjugation for a pair of functions and obtain a formula for the determination of its index.