A new generalized <i>θ</i> -conformable calculus and its applications in mathematical physics
Abd‐Allah Hyder, Ahmed H. Soliman
Abstract
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo accent="false">′</mml:mo> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>G</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> –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.