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In the present paper, we introduce a two-order nonlinear fractional sequential Langevin equation using the derivatives of Atangana-Baleanu and Caputo-Fabrizio. The existence of solutions is proven using a fixed point theorem under a weak topology, and an illustrative example is then given. Furthermore, we present new fractional versions of the Adams-Bashforth three-step approach for the Atangana-Baleanu and Caputo derivatives. New nonlinear chaotic dynamics are performed by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we first obtain Hermite-Hadamard-Fejer inequalities for co-ordinated convex functions in a rectangle from the plane ℝ². Moreover, we give the some refinement of these obtained Hermite-Hadamard-Fejer inequalities utilizing two mapping. The inequalities obtained in this study provide generalizations of some result given in earlier works. [ABSTRACT FROM AUTHOR]

In this study, we obtain some new weighted inequalities of Grüss type for functions of two independent variables. Special cases of the results presented here reduce the results given in earlier works. [ABSTRACT FROM AUTHOR]