In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...

The isothermal gas sphere is well known as a powerful tool to model many problems in astrophysics, physics, chemistry, and engineering. This singular differential equation has not an exact solution solved only by numerical approximate methods. In the present paper within framework of Newtonian hydrostatic equilibrium, we have developed general analytical formulations for fractional sphere. To o...

We study the conformable fractional (CF) Dirac system with separated boundary conditions on an arbitrary time scale [Formula: see text]. Then we extend some basic spectral properties of the classical Dirac system to the CF case. Eventually, some asymptotic estimates for the eigenfunction of the CF Dirac eigenvalue problem are obtained on [Formula: see text]. So, we provide a constructive proced...

The Riemann wave equation is an intriguing nonlinear in the areas of tsunamis and tidal waves oceans, electromagnetic transmission lines, magnetic ionic sound radiations plasmas, static uniform media, etc. In this innovative research, analytical solutions fractional with a conformable derivative were retrieved as special case, broad-spectrum unknown parameters established improved (G’/G)-expans...

In this contribution, we develop the Maxwell generalized thermodynamical relations via the metric derivative model upon the mapping to a continuous fractal space. This study also introduces the total q-derivative expressions depending on two variables, to describe nonextensive statistical mechanics and also the α-total differentiation with conformable derivatives. Some results in the literature...

In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula.