This paper contains a variety of new integral inequalities for (s,m)-convex functions using Caputo fractional derivatives and Caputo–Fabrizio operators. Various generalizations Hermite–Hadamard-type containing operators are derived those whose (s,m)-convex. Inequalities involving the digamma function special means deduced as applications.

We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of relations nth-weighted integrals and derivatives. As an application, mean value theorems operators are obtained. Direct corollaries allow one to obtain recent Caputo–Fabrizio, Atangana–Baleanu–Caputo (ABC) ABC

The time-fractional diffusion-wave equation is considered in a half-plane. The Caputo fractional derivative of the order 0 < α < 2 is used. Several examples of problems with Dirichlet and Neumann boundary conditions are solved using the Laplace integral transform with respect to time and the Fourier transforms with respect to spatial coordinates. The solution is written in terms of the Mittag-L...

This paper develops appropriate boundary conditions for the two-sided fractional diffusion equation, where the usual second derivative in space is replaced by a weighted average of positive and negative fractional derivatives. Mass preserving, reflecting boundary conditions for two-sided fractional diffusion involve a balance of left and right fractional derivatives at the boundary. Stable, con...

In order to investigate the honeybee population dynamics, many differential equation models were proposed. Fractional derivatives incorporate history of dynamics. We numerically study inverse problem parameter identification in with Caputo and Caputo–Fabrizio operators. use a gradient method minimizing quadratic cost functional. analyze compare results for integer (classic) fractional models. T...

‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...

In this paper, we propose an efficient alternating direction implicit (ADI) Galerkin method for solving the time-fractional partial differential equation with damping, where the fractional derivative is in the sense of Caputo with order in (1, 2). The presented numerical scheme is based on the L2-1σ method in time and the Galerkin finite element method in space. The unconditional stability and ...