Research Article A Study on the Solutions of a Multiterm FBVP of Variable Order Zoubida Bouazza, 1 Sina Etemad, 2 Mohammed Said Souid, 3 Shahram Rezapour , 2,4 Francisco Martínez, 5 and Mohammed K. A. Kaabar 6 1 Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, Algeria 2 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran 3 Department of Economic Sciences, University of Tiaret, Algeria 4 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan 5 Department of Applied Mathematics and Statistics, Technological University of Cartagena, Cartagena 30203, Spain 6 Jabalia Camp, United Nations Relief and Works Agency (UNRWA) Palestinian Refugee Camp, Gaza Strip Jabalya, State of Palestine Correspondence should be addressed to Shahram Rezapour; rezapourshahram@yahoo.ca and Mohammed K. A. Kaabar; mohammed.kaabar@wsu.edu Received 25 March 2021; Accepted 27 April 2021; Published 24 May 2021 Academic Editor: Jiabin Zuo Copyright © 2021 Zoubida Bouazza et al. This 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 the present research study, for a given multiterm boundary value problem (BVP) involving the nonlinear fractional differential equation (NnLFDEq) of variable order, the uniqueness-existence properties are analyzed. To arrive at such an aim, we first investigate some specifications of this kind of variable order operator and then derive required criteria confirming the existence of solution. All results in this study are established with the help of two fixed-point theorems and examined by a practical example. 1. Introduction The first historical resource to the invention of fractional derivative (FrDr) was proposed in 1695, when L’Hopital pro- posed the question about the meaning of d σ y/dx σ if σ = 1/2. The proposed FrDr’s definitions are classified into two cate- gories: global nature and local nature. On the one hand, under the global one, the FrDr is defined as integral, Fourier, or Mellin transformations; hence, its nonlocal characteristic is given with a memory. On the other hand, under the local one, FrDr is relied on a local definition through certain incre- mental ratios. As a result of this classical formulation, frac- tional calculus (FrCa) has appeared since the time of well- known mathematicians such as Lacroix, Fourier, Liouville, Euler, Laplace, and Abel until the creation of the first modern fractional definitions of Caputo and Riemann-Liouville. The FrCa theory is a representation of a powerful tool of mathematical analysis for investigating the integrals and derivatives of arbitrary order, which constitutes the unifying and generalizing element of the integer-order differentiation and n-fold integration [1, 2]. Studying fractional integrals and derivatives was only devoted to the theoretical mathe- matical context. However, their applications have been recently seen in multidisciplinary sciences such as theoretical physics, entropy theory, fluid mechanics, biology, and image processing [3–13]. Furthermore, studying both of the theoretical and practi- cal aspects of fractional differential equations (FDEqs) has become a focus of international academic research [14–18]. A recent improvement on this investigation is the consider- ation of the notion of variable order operators. In this sense, various definitions of fractional operators involving the vari- able order have been introduced. This type of operators which are dependent on their power-law kernel can describe some hereditary specifications of numerous processes and phenomena [19, 20]. In general, it is often difficult to find the analytical solution of FDEqs of variable order; therefore, numerical methods for the approximation of FDEqs of vari- able order are widespread. Regarding the study of solutions’ existence to the problems of variable order, we refer to [21– Hindawi Journal of Function Spaces Volume 2021, Article ID 9939147, 9 pages https://doi.org/10.1155/2021/9939147