The main objective of this paper is to use the generalized proportional Hadamard fractional integral operator establish some new inequalities for extended Chebyshev functionals. In addition, we investigate positive continuous functions by employing a operator. findings study are theoretical but have potential help solve additional practical problems in mathematical physics, statistics, and appr...

In this paper, we consider a non-homogeneous time–space-fractional telegraph equation in n-dimensions, which is obtained from the standard by replacing first- and second-order time derivatives Caputo fractional of corresponding orders, Laplacian operator Sturm–Liouville defined terms right left Riemann–Liouville derivatives. Using method separation variables, derive series representations solut...

in this paper, the homotopy perturbation method (hpm) is applied to obtain an approximate solution of the fractional bratu-type equations. the convergence of the method is also studied. the fractional derivatives are described in the modi ed riemann-liouville sense. the results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional...

In this article, we consider the multi-point boundary-value problem for nonlinear fractional differential equations with p-Laplacian operator: D 0+ φp(D α 0+ u(t)) = f(t, u(t), Dα−2 0+ u(t), Dα−1 0+ u(t), D 0+ u(t)), t ∈ (0, 1), u(0) = u′(0) = D 0+ u(0) = 0, Dα−1 0+ u(1) = m X i=1 σiD α−1 0+ u(ηi), where 2 < α ≤ 3, 0 < β ≤ 1, 3 < α+β ≤ 4, Pm i=1 σi = 1, D α 0+ is the standard Riemann-Liouville ...

Although there have existed some numerical algorithms for the fractional differential equations, developing high-order methods (i.e., with convergence order greater than or equal to 2) is just the beginning. Lubich has ever proposed the high-order schemes when he studied the fractional linear multistep methods, where he constructed the pth order schemes (p = 2, 3, 4, 5, 6) for the αth order Rie...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

We give a natural definition of the Morrey spaces for Radon measures which may be non-doubling but satisfy the growth condition. In these spaces we investigate the behavior of the maximal operator, the fractional integral operator, the singular integral operator and their vector-valued extensions.

In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given. 

In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modied Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional p...