Research Article Fractional Order Airy’s Type Differential Equations of Its Models Using RDTM Daba Meshesha Gusu , 1 Dechasa Wegi, 2 Girma Gemechu, 2 and Diriba Gemechu 2 1 Department of Mathematics, Ambo University, Ambo, Ethiopia 2 Department of Mathematics, Mettu University, Metu, Ethiopia Correspondence should be addressed to Daba Meshesha Gusu; dabam7@gmail.com Received 19 June 2021; Revised 15 August 2021; Accepted 19 August 2021; Published 10 September 2021 Academic Editor: Kamal Shah Copyright © 2021 Daba Meshesha Gusu et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we propose a novel reduced differential transform method (RDTM) to compute analytical and semianalytical approximate solutions of fractional order Airy’s ordinary differential equations and fractional order Airy’s and Airy’s type partial differential equations subjected to certain initial conditions. e performance of the proposed method was analyzed and compared with a convergent series solution form with easily computable coefficients. e behavior of approximated series solutions at different values of fractional order α and its modeling in 2-dimensional and 3-dimensional spaces are compared with exact solutions using MATLAB graphical method analysis. Moreover, the physical and geometrical interpretations of the computed graphs are given in detail within 2- and 3-dimensional spaces. Accordingly, the obtained approximate solutions of fractional order Airy’s ordinary differential equations and fractional order Airy’s and Airy’s type partial differential equations subjected to certain initial conditions exactly fit with exact solutions. Hence, the proposed method reveals reliability, effectiveness, efficiency, and strengthening of computed mathematical results in order to easily solve fractional order Airy’s type differential equations. 1. Introduction e fractional calculus is a generalization of the differen- tiation and integration to arbitrary noninteger order. It is the theory of integrals and derivatives of arbitrary order which unifies and generalizes the concepts of integer order dif- ferentiation and n-fold integration. Currently, the theory of fractional differentiation has gained much more attention as the fractional order system response ultimately converges to the integer order equations. e no analytical solution method was available for such type of equations before the nineteenth century as explained in [1]. In recent past years, the glorious developments have been investigated in the field of fractional calculus and fractional differential equations. Several real phenomena emerging in engineering and science fields can be demon- strated successfully by developing models using the frac- tional calculus theory. Some of these are time fractional heat equations, time fractional heat-like equations, time frac- tional wave equations, time fractional telegraphic equation, fractional order Airy’s ordinary differential equation, time fractional Airy’s partial differential equations, and so on. ese equations are represented by linear and nonlinear differential equations, and since they have so many appli- cations in the field of science, solving such fractional dif- ferential equations is very important. e main advantage of fractional order differential equations is that it is a global operator and produces accurate as well as stable results. erefore, these equations constitute an important class of differential equations, and for some recent work, we refer the readers to study the work in [2–9]. e term Airy differential equation was first coined by George Biddell Airy, who was particularly involved in optics [10]. He also had an interest in the calculation of light in- tensity in the area of a caustic surface. A number of scholars have acknowledged that the e Airy equation has a Hindawi Mathematical Problems in Engineering Volume 2021, Article ID 3719206, 21 pages https://doi.org/10.1155/2021/3719206