... the **multidimensional** **time**- **fractional** **equation** with Laplace or Dirac operators, where the two **time**-**fractional** derivatives of orders α ∈]0, 1] and β ∈]1, 2] are in the Caputo ...

... the **multidimensional** **time**-**fractional** **equation** of order 2α, α ∈]0, 1], where the two **time**-**fractional** derivatives are in the Caputo ...

... In this paper we present integral and series representations for the fundamental solution of the **time** **fractional** diffusion **equation** in an arbitrary dimension. The series representation obtained ...

... inhomogeneous **time**-**fractional** telegraph **equation** with Caputo derivatives, and obtained a general representation of regular solution in rectangular domain in terms of fundamental solution and ...

... order. **Fractional** order calculus has become very popular in recent years, due to its demonstrated applications in many fields of applied sciences and engineering, such as the spread of contaminants in underground ...

... Abstract— In this paper, we have applied an accurate and efficient homotopy analysis method (HAM) to find the approximate/analytical solutions for space and **time** **fractional** reaction- diffusion equations ...

... posed by Becker and D¨ oring amounted to [6, 28], since they considered the case where the concentration of monomers stay constant in **time**. Physically this can only be implemented by coupling the system to a ...

... of **fractional** differential equations, compared with the classical theory of differential equations, is a field of research only on its initial stage of development, calling great interest to many mathematicians [ ...

... Consequently, according to the well-known theory of general metric spaces, we have for T the fundamental concepts such as open balls (intervals), neighborhoods of points, open sets, closed sets, compact sets, etc. In ...

... Littman, Near optimal time boundary controllability for a class of hyperbolic equations, In Lecture Notes in Control and Information Sciences, pp... Miranda, ContrSlabilit~ e[r] ...

... For almost 300 years **fractional** derivative was seen as an interesting, but abstract, mathematical concept. The development of the **fractional** calculus was mainly in the hands of mathematicians. This led to a ...

... by **fractional** dierential equations has been motiva- tion for the study and application of **fractional** calcu- ...the **fractional** calculus to science and engineering problems needs a coherent ...

... vast **time** and frequency scales with very concise and computable models [4], [8], [12], [13], [16], [26], [29], [47]–[50], ...the **fractional** systems exhibits both short and long term ...of **time** ...

... **Fractional** Brownian motion (fBm), 1/f noises, self-similaririty and long range dependence are inter- connected notions and appear in a variety of contexts [1–3]. The starting point was the introduction of the fBm ...

... Although the comparison was performed on ANN-based filters, the experimental results confirm that the enhanced Bayesian method can predict chaotic **time** series more effectively in terms of SMAPE and RMSE indices ...

... Abstract —In this paper we prove the existence of solution to the periodic Boltzmann BGK model (Bhatnagar-Gross-Krook) coupled with poisson’s **equation** in one space dimension. BGK model is a collision operator for ...

... The roots of the calculus of variations appear in works of Greek thinkers, such as Queen Dido or Aristotle in the late of the 1st century BC. During the 17th century, some physicists and mathematicians (Galileo, Fermat, ...

... Investigations on earthquake predictions are based on the assumption that all of the regional factors can be filtered out and general information about the earthquake precursory patterns can be extracted (Geller et al., ...

... diffusion **equation** with distributed-order of derivative in **time** has been presented, and its unconditional stability and convergence were ...the **time** derivatives since it will be convenient to use ...

... A **time** scale is a model of **time**, and the theory has found important applications in several contexts that require simultane- ous modeling of discrete and continuous ...