Fej'{e}r  Hadamard  inequality is generalization of Hadamard inequality. In this paper we prove certain Fej'{e}r  Hadamard  inequalities for $k$-fractional integrals. We deduce Fej'{e}r  Hadamard-type  inequalities for Riemann-Liouville fractional integrals. Also as special case Hadamard inequalities for $k$-fractional as well as fractional integrals are given.

<p style='text-indent:20px;'>In this paper we study the Riemann-Liouville fractional integral of order <inline-formula><tex-math id="M1">\begin{document}$ \alpha>0 $\end{document}</tex-math></inline-formula> as a linear operator from id="M2">\begin{document}$ L^p(I,X) into itself, when id="M3">\begin{document}$ 1\leq p\leq \infty $\end{document}</te...

For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of operator theory in Sobolev spaces. Our provides feasible extension classical Caputo Riemann–Liouville within spaces orders, including negative ones. approach enables unified treatment for calculus equations. We formulate initial value problems ordinary equations boundary partial to pr...

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract This paper investigates a boundary value problem of Caputo type sequential fractional differential equations supplemented with nonlocal Riemann-Liouville f...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...