## THERMAL SCIENCE

International Scientific Journal

### VARIABLE-ORDER FRACTIONAL CREEP MODEL OF MUDSTONE UNDER HIGH-TEMPERATURE

**ABSTRACT**

In order to study the properties of high-temperature creep for mudstone, MTS810 electro-hydraulic servo material test system and MTS652.02 high temperature furnace are utilized for the creep test of mudstone at 700°C. Considering the visco-elastic-plastic characteristics and the damage effect, the variable-order fractional creep model is established to research the creep character, and it is found that the proposed model can be well fitting of our experimental results. Especially, variable-order function can be used to analyze and study the viscoelastic property evolution of mudstone in process of high-temperature creep. Compositions of mudstone are distinguished by X-ray diffraction technology. The presence of the illite under high temperatures can be used for explaining the viscous feature prevails over the elastic ones in viscoelastic properties.

**KEYWORDS**

PAPER SUBMITTED: 2017-03-10

PAPER REVISED: 2017-05-01

PAPER ACCEPTED: 2017-05-15

PUBLISHED ONLINE: 2017-12-02

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**Supplement 1**, PAGES [S343 - S349]

- Li, Y., et al., A Survey on Fractional-Order Iterative Learning Control, Journal of Optimization Theory and Applications, 156 (2013), 1, pp. 127-140
- Yang, X. J., et al., On a Fractal LC-Electric Circuit Modeled by Local Fractional Calculus, Communications in Nonlinear Science and Numerical Simulation, 47 (2017), June, pp. 200-206
- Yang, X. J., A New Integral Transform Operator for Solving the Heat-diffusion Problem, Applied Mathematics Letters, 64 (2017), Feb., pp. 193-197
- Xu, M. Y., Tan, W., Intermediate Processes and Critical Phenomena: Theory, Method and Progress of Fractional Operators and Their Applications to Modern Mechanics, Science China Physics, Mechanics and Astronomy, 49 (2006), 3, pp. 257-272
- Mainardi, F., An Historical Perspective on Fractional Calculus in Linear Viscoelasticity, Fractional Calculus and Applied Analysis, 15 (2012), 4, pp.712-717
- Paola, M. D., et al., Fractional Differential Equations and Related Exact Mechanical Models, Computers and Mathematics with Applications, 66 (2013), 5, pp. 608-620
- Bagley, R. L., et al., A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity, Journal of Rheology, 27 (1983), 3, pp. 608-620
- Coimbra, C. F. M., Mechanics with Variable-Order Differential Operators, Annalen der Physik, 12 (2003), 11-12, pp. 692-703
- Soon, C. M., et al., The Variable Viscoelasticity Oscillator, Annalen der Physik, 12 (2005), 6, pp. 378-389
- Ramirez, L. E., Coimbra, C. F., A Variable Order Constitutive Relation for Viscoelasticity, Annalen der Physik, 16 (2007), 7-8, pp. 543-552
- Atangana, A., Cloot, A. H., Stability and Convergence of the Space Fractional Variable-order Schroedinger Equation, Advances in Difference Equations, 80, (2013), 1, pp.1-10
- Bazhlekova, E. G., Dimovski, I. H., Exact Solution for the Fractional Cable Equation with Nonlocal Boundary Conditions, Central European Journal of Physics, 11 (2013), 10, pp. 1304-1313
- Sun, H. G., et al., A Comparative Study of Constant-Order and Variable-Order Fractional Models in Characterizing Memory Property of Systems, The European Physical Journal Special Topics 193, (2011), 1, pp. 185-192
- Razminia, A, et al., Solution Existence for Non-Autonomous Variable-Order Fractional Differential Equations, Mathematical and Computer Modelling, 55 (2011), 3, pp. 1106-1117
- Zhang, S., Existence and Uniqueness Result of Solutions to Initial Value Problems of Fractional Differential Equations of Variable-Order, Journal of Fractional Calculus and Applications, 4, (2013), 1, pp. 82-98
- Yang, X. J., Machado, J. A. T., A New Fractional Operator of Variable Order: Application in the Description of Anomalous Diffusion, Physica A: Statistical Mechanics and its Applications, 481 (2017), Sept., pp. 276-283
- Valerio, D., Da Costa, J. S., Variable-Order Fractional Derivatives and Their Numerical Approximations, Signal Processing, 91 (2011), 3, pp. 470-483
- Bhrawy, A. H., Zaky, M. A., Numerical Simulation for Two-Dimensional Variable-Order Fractional Nonlinear Cable Equation, Nonlinear Dynamics, 80 (2015), 1-2, pp. 101-116
- Yang, X. J., New Rheological Problems Involving General Fractional Derivatives within Nonsingular Power-Law Kernel, Proceedings of the Romanian Academy - Series A, 69, (2017), 3, in press
- Yang, X. J., New General Fractional-Order Rheological Models within Kernels of Mittag-Leffler Functions, Romanian Reports in Physics, 69, (2017), 4, Article ID 118
- Yang, X. J., et al., New Rheological Models within Local Fractional Derivative, Romanian Reports in Physics, 69 (2017), 3, pp. 113
- Yang, X. J., et al., Anomalous Diffusion Models with General Fractional Derivatives within the Kernels of the Extended Mittag-Leffler Type Functions, Romanian Reports in Physics, 69, (2017), 4, Article ID 115