Retraction Note to: Derivative with two fractional orders: A new avenue of investigation toward revolution in fractional calculus
نویسندگان
چکیده
In order to describe more complex problems using the concept of fractional derivatives, we introduce in this paper fractional derivatives with orders. The new definitions are based upon power law together generalized Mittag-Leffler function. first is included power function and second one Each therefore plays an important role while modeling, for instance, two layers with different properties. This case, thermal science a reaction diffusion within media Another case that groundwater flowing aquifer where geological formation formed The presents operators will open doors research and investigations modeling real world problems. Some useful properties new presented, particular their relationship existing integral transforms, namely Laplace, Sumudu, Mellin Fourier transforms. numerical approximation presented. We apply on model plume degradation limited sorption solve numerically some numerical simulations. simulation leaves no doubt believing operators powerfull mathematical tools able portray complexes world
منابع مشابه
Fractional Derivative as Fractional Power of Derivative
Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.
متن کاملFractional Ince equation with a Riemann-Liouville fractional derivative
We extend the classical treatment of the Ince equation to include the effect of a fractional derivative term of order a > 0 and amplitude c. A Fourier expansion is used to determine the eigenvalue curves að Þ in function of the parameter , the stability domains, and the periodic stable solutions of the fractional Ince equation. Two important observations are the detachment of the eigenvalue cur...
متن کاملAnomalous diffusion with ballistic scaling: A new fractional derivative
Anomalous diffusion with ballistic scaling is characterized by a linear spreading rate with respect to time that scales like pure advection. Ballistic scaling may be modeled with a symmetric Riesz derivative if the spreading is symmetric. However, ballistic scaling coupled with a skewness is observed in many applications, including hydrology, nuclear physics, viscoelasticity, and acoustics. The...
متن کاملCalculus of variations with fractional derivatives and fractional integrals
We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
متن کاملFractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
and Applied Analysis 3 2. Preliminaries In this section, we present definitions and properties of generalized fractional operators. As particular cases, by choosing appropriate kernels, these operators are reduced to standard fractional integrals and fractional derivatives. Other nonstandard kernels can also be considered as particular cases. For more on the subject of generalized fractional ca...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Physical Journal Plus
سال: 2021
ISSN: ['2190-5444']
DOI: https://doi.org/10.1140/epjp/s13360-020-00965-w