The use of non-local operators, defining Riemann–Liouville or Caputo derivatives, is a very useful tool to study problems involving non-conventional diffusion problems. case electric circuits, ruled by non-integer derivatives capacitors with fractional dielectric permittivity, fairly natural frame relevant applications. We techniques, generalized exponential obtain suitable solutions for this t...

This study presents an efficient method that is suitable for differential equations, both with integer-order and fractional derivatives. examines the construction of solutions equations are associated varying delay proportional to independent variable using a hybrid Sumudu transform method. considers Caputo derivatives orders their applications in Nuclear Physics. The application indicates have...

‎It is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎For‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎This paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎The fractional derivatives are described...

and Applied Analysis 3 The rest of this paper is organized as follows. In Section 2, preliminaries and problem statement are given. In Section 3, the consensus conditions are derived by using linear matrix inequality approach and matrix’s singular value decomposition. In Section 4, a simulation example is provided to show the advantages of the obtained results. Conclusions are presented in Sect...

In this paper, an approximate formula of the fractional derivatives (Caputo sense) is derived. The proposed formula is based on the generalized Laguerre polynomials. Special attention is given to study the convergence analysis of the presented formula. The spectral Laguerre collocation method is presented for solving a class of fractional optimal control problems (FOCPs). The properties of Lagu...

In this article, the variational homotopy perturbation method (VHPM) [proposed in A. Noor et al., Mathematical Problems in Engineering, 1155(10) (2008), 696734] is adopted for solving linear fractional partial differential equations. The aim of this letter is to present an efficient and reliable treatment of the VHPM for the linear fractional partial differential equations. The fractional deriv...

In the paper, we present some applications and features related with the new notions of fractional derivatives with a time exponential kernel and with spatial Gauss kernel for gradient and Laplacian operators. Specifically, for these new models we have proved the coherence with the thermodynamic laws. Hence, we have revised the standard linear solid of Zener within continuum mechanics and the m...

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The ...

Based on He's variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of th...

*Correspondence: [email protected] Department of Science, Huaihai Institute of Technology, Cangwu Road, Lianyungang, 222005, China Abstract We apply the Chebyshev polynomial-based differential quadrature method to the solution of a fractional-order Riccati differential equation. The fractional derivative is described in the Caputo sense. We derive and utilize explicit expressions of weighting coef...