Abdelkader Moumen

Recently, many scientists have studied a wide range of strategies for solving characteristic types of symmetric differential equations, including symmetric fractional differential equations (FDEs). In our manuscript, we obtained sufficient conditions to prove the existence and uniqueness of solutions (EUS) for FDEs in the sense ψ-Caputo fractional derivative (ψ-CFD) in the second-order 1<α<2. We know that ψ-CFD is a generalization of previously familiar fractional derivatives: Riemann-Liouville and Caputo. By applying the Banach fixed-point theorem (BFPT) and the Schauder fixed-point theorem (SFPT), we obtained the desired results, and to embody the theoretical results obtained, we provided two examples that illustrate the theoretical proofs.

In this paper, we investigate a new class of nonlinear fractional integrodifferential systems that includes the Ψ-Riemann–Liouville fractional integral term. Using the technique of upper and lower solutions, the solvability of the system is examined. We add two examples to demonstrate and validate the main result. The main results highlight crucial contributions to the general theory of fractional differential equations.

Integral inequalities are a powerful tool for estimating errors of quadrature formulas. In this study, some symmetric dual Simpson type integral inequalities for the classes of s-convex, bounded and Lipschitzian functions are proposed. The obtained results are based on a new identity and the use of some standard techniques such as Hölder as well as power mean inequalities. We give at the end some applications to the estimation of quadrature rules and to particular means.

Various scholars have lately employed a wide range of strategies to resolve specific types of symmetrical fractional differential equations. In this paper, we propose a new fractional identity for multiplicatively differentiable functions; based on this identity, we establish some new fractional multiplicative Bullen-type inequalities for multiplicative differentiable convex functions. Some applications of the obtained results are given.