Special Issue "Interval Arithmetic with Applications to Physical Phenomena"

Submission Deadline: 01 February 2021
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Guest Editors
Dr. Ali Ahmadian, National University of Malaysia, Malaysia.
Dr. Soheil Salahshour Soheil Salahshour, Bahcesehir University, Turkey.
Prof. Ahmad Azar, Prince Sultan University, Kingdom Saudi Arabia.


One of the important topics in the applied science is dynamic systems and their applications. If these systems are involved with complex-uncertain data then they will be more important and practical. Because the real-life problems work with this type of data and most of them cannot be solved exactly and easily and sometimes they are impossible to solve. In this regard, role of employing differential equations with uncertain parameters are inevitable. Interval mathematical modeling has not been considered enough for a long time. However, in the recent years, the scientists found the applicability of this significant notion measure uncertainties in the mathematical modeling with interval parameters. Therefore, a number of researches have been done in this regard to analyze the mathematical systems based on the interval parameters and study the real-world systems based on fuzzy mathematical modeling.


Specific topics of interest include (but are not limited to):

• Foundation of Interval arithmetic (Interval arithmetic operations, Generalized Hukuhara difference, Differentiation of interval-valued functions, variant of constraint interval arithmetic, etc.) 

• Interval ordinary differential equations (Existence, Uniqueness and Stability of the solution)

• Interval integral differential equations in combination with machine learning algorithms

• Fractional calculus for interval-valued functions

• Interval dynamical systems and their relevant approximate solutions

• Spectral solutions of interval integer and fractional models arising in the physical models 

• Interval arithmetic to model the viscoelastic behavior of the dynamic systems

• Numerical solutions of Hybrid Interval differential equations

• Approximate solutions of interval integro-differential equations

• Interval functional, stochastic, fractional and random differential equations with their numerical solutions

Interval arithmetic, dynamical systems, physical problems, fractional calculus, numerical simulations, mathematical modeling, machine learning algorithms

Published Papers
  • Accurate Fault Location Modeling for Parallel Transmission Lines Considering Mutual Effect
  • Abstract A new accurate algorithms based on mathematical modeling of two parallel transmissions lines system (TPTLS) as influenced by the mutual effect to determine the fault location is discussed in this work. The distance relay measures the impedance to the fault location which is the positive-sequence. The principle of summation the positive-, negative-, and zero-sequence voltages which equal zero is used to determine the fault location on the TPTLS. Also, the impedance of the transmission line to the fault location is determined. These algorithms are applied to single-line-to-ground (SLG) and double-line-to-ground (DLG) faults. To detect the fault location along the transmission… More
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