In this work, a new generalized concept of conformable derivative is given and named generalized θ –conformable derivative (GTCD). Several properties are studied such as the chain rule, the quotient rule, the product rule, the Rolle’s theorem, the mean value theorem and the fundamental theorems of calculus. Also, the geometrical and physical interpretations of the GTCD are presented. It is very easy to see that the GTCD is comprehensive and includes many past derivatives as special cases. An application of the generalized θ –conformable derivatives (GTCDs) is presented along with the G ′ / G , 1 / G –approach to construct a novel gathering of exact solutions for the nonlinear (2+1)-dimensional biological population model (BPM) involving GTCDs. Moreover, some comparisons and graphical interpretations are given to support our results related to the (2+1)-dimensional BPM. All acquired results regarding the GTCD show its validity to applying in many problems in mathematical physics, engineering, biology and others.

We look at fractional Langevin equations (FLEs) with generalized proportional Hadamard–Caputo derivative of different orders. Moreover, nonlocal integrals and nonperiodic boundary conditions are considered in this paper. For the proposed equations, the Hyres–Ulam (HU) stability, existence, and uniqueness (EU) of the solution are defined and investigated. In implementing our results, we rely on two important theories that are Krasnoselskii fixed point theorem and Banach contraction principle. Also, an application example is given to bolster the accuracy of the acquired results.

With the assistance of Hermite transform, we use the Exp-function technique to solve the Wick-type stochastic KdV equation with a generalized type of conformable derivatives. The exact solutions of the stochastic KdV equation are obtained in a white noise environment. Two new kinds of Brownian motion functional solutions, including soliton and periodic solutions are presented. The graphs for a portion of these exact solutions have been given by picking peculiar values of the existing parameters to visualize the proposed technique of the given KdV equation.

We prove some n-tupled coincidence point results whenever n is even. We give here several new definitions like n-tupled fixed point, n-tupled coincidence point, and so forth. The main result is supported with the aid of an illustrative example.

In this paper, we point out that some recent results of Vijaywar et al. (Coincidence and common fixed point theorems for hybrid contractions in symmetric spaces, Demonstratio Math. 45 (2012), 611-620) are not true in their present form. With a view to prove corrected and improved versions of such results, we introduce the notion of common limit range property for a hybrid pair of mappings and utilize the same to obtain some coincidence and fixed point results for mappings defined on an arbitrary set with values in symmetric (semi-metric) spaces. Our results improve, generalize and extend some results of the existing literature especially due to Imdad et al., Javid and Imdad, Vijaywar et al. and some others. Some illustrative examples to highlight the realized improvements are also furnished.