A new generalized θ-conformable calculus and its applications in mathematical physics

Abstract

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.

Conformable fractional versions of Hermite–Hadamard-type inequalities for twice-differentiable functions

“…Furthermore, in [1] the researchers showed that the conformable approach in [15] cannot yield good results when compared to the Caputo definition via specific mappings. This imperfection in the conformable description is avoided by some refinements of the conformable approach [9,22].…”

Novel improved fractional operators and their scientific applications

“…Presently, it turns out that the LCD generalizes the traditional Newton-Leibniz derivative on a nonzero domain, but it has no correlation at zero. So, it is subjected to some criticism [1,26]. This blemish in the LCD was evaded by a new local generalized conformable derivative (LGCD), proposed by Zhao and Luo [55].…”

“…This blemish in the LCD was evaded by a new local generalized conformable derivative (LGCD), proposed by Zhao and Luo [55]. Therefore the locality and inclusiveness advantages of the LGCD give it the entitlement to occupy the place of the LCD [26,56]. Moreover, the LGCD provides a new application environment to gain some general results for many physical evolution models [25,27,55,56].…”

Analytical manner for abundant stochastic wave solutions of extended KdV equation with conformable differential operators

“…Lately, applications of generalized calculus are frequently appeared to unveil the behavior of multiple nonlinear phenomena. [20][21][22][23] Various types of generalized derivatives were introduced ever, similar to Grunwald-Letnikov, Riesz, Riemann-Liouville, Caputo, and so forth. Most of them are described by methods for generalized integrals; hence, they obtain nonlocal properties from classic integrals.…”

“…Generalized calculus is an astonishing and ground‐breaking subject for showing nonlinear systems. Lately, applications of generalized calculus are frequently appeared to unveil the behavior of multiple nonlinear phenomena 20‐23 . Various types of generalized derivatives were introduced ever, similar to Grunwald‐Letnikov, Riesz, Riemann‐Liouville, Caputo, and so forth.…”