Abstract
Abstract In this work, the well known invariant subspace method has been modified and extended to solve some partial differential equations involving Caputo-Fabrizio (CF) or Atangana-Baleanu (AB) fractional derivatives. The exact solutions are obtained by solving the reduced systems of constructed fractional differential equations. The results show that this method is very simple and effective for constructing explicit exact solutions for partial differential equations involving new fractional derivatives with nonlocal and non-singular kernels, such solutions are very useful to validate new numerical methods constructed for solving partial differential equations with CF and AB fractional derivatives.
Highlights
Fractional calculus provides an important characteristic to describe the complicated physical phenomena with memory effects
The fractional calculus is becoming increasingly used as a modeling tool in physics, engineering and control processing in various fields of sciences such as fluid dynamics, plasma physics, mathematical biology and chemical kinetics, diffusion, etc [1,2,3,4]
Caputo and Fabrizio defined a new fractional derivative without singular kernel [10] named Caputo-Fabrizio derivative with specific properties, the derivative of a constant is zero and the initial conditions used in the fractional differential equations having a physical interpretation
Summary
Fractional calculus provides an important characteristic to describe the complicated physical phenomena with memory effects For this reason, the fractional calculus is becoming increasingly used as a modeling tool in physics, engineering and control processing in various fields of sciences such as fluid dynamics, plasma physics, mathematical biology and chemical kinetics, diffusion, etc [1,2,3,4]. Recent investigations show that the invariant subspace method, developed by V.A. Galaktionov and S.R. Svirshchevski [17], is an effective tool to construct exact solutions of some fractional partial differential equations with Caputo fractional derivative.
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