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...

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.

In this paper, we present an analytical method to solve a time-conformable fractional telegraph equation with three boundary conditions namely, Dirichlet, Neumann and Robin. This based on Fourier conformable calculus properties. We give examples validate method.