Counting polynomials find their way into chemical graph theory through quantum chemistry
in two ways: as approximate solutions to the Schrödinger equation or by storing information …

Water is one of the main constituents on earth for a living. The Advection Diffusion Equation
(ADE) serves as an essential water standard model in environmental engineering since …

This study presents a new efficient collocation approach to handle the nonlinear generalized
fractional Riccati equation. The linearization formula of the product of two shifted Chebyshev …

Abstract Caputo and Riemann–Liouville (R–L) are the most commonly used fractional
derivative operators in the field of fractional calculus. We present here two higher-order …

Objectives: Introduction to new numerical techniques to solve differential, difference, and
integro-differential equations (IDEs) are always remaining the thrust area of research for …

In this paper, we presented a new analytical method for one of the rapidly emerging
branches of fractional calculus, the distributed order fractional differential equations (DFDE) …

In this paper, we derive the exact analytical solution for the periodic oscillations of a
nonlinear mechanical oscillator that is capable of describing phase transition phenomenon …