In this article, we establish bounds of sum of the left and right sided Riemann Liouville (RL) fractional integrals and related inequalities in general form. A new and novel approach is followed to obtain these results for general Riemann Liouville (RL) fractional integrals. Monotonicity and convexity of functions are used with some usual and straight forward inequalities. The presented results are also have connection with some known and already published results. Applications and motivations of presented results are briefly discussed.

In the present research, we develop some integral inequalities of Hermite-Hadamard type for differentiable η-convex functions. Moreover, our results include several new and known results as particular cases.

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The Klein–Fock–Gordon equation (KFGE), defined as the equation of relativistic wave related to NLEEs, has numerous implications for energy particle physics and is useful as a model for several types of matter, with deviation in the basic stuffs of particles and in crystals. In this work, the Sardar subequation method (SSM) is used for finding the solution of this KFGE. The advantage of SSM is that it provides many different kinds of solitons, such as dark, bright, singular, periodic singular, combined dark–singular and combined dark–bright solitons. The results show that the SSM is very reliable, simple and can be functionalized to other nonlinear equations. It is verified that all the attained solutions are stable by modulation instability process. To enhance the physical description of solutions, some 3D, contour and 2D graphs are plotted by taking precise values of parameters using Maple 18.

The aim of this paper is to introduce the definition of a generalized strongly p-convex function for higher order. We will develop some basic results related to generalized strongly p-convex function of higher order. Moreover, we will develop Hermite–Hadamard-, Fejér-, and Schur-type inequalities for this generalization.