Citation: Al-Rab’a, A.; Al-Sharif, S.; Al-Khaleel, M. Double Conformable Sumudu Transform. Symmetry 2022, 14, 2249. https://doi.org/ 10.3390/sym14112249 Academic Editors: Ioan Ra¸ sa and Jan Awrejcewicz Received: 29 August 2022 Accepted: 13 October 2022 Published: 26 October 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). symmetry S S Article Double Conformable Sumudu Transform Abdallah Al-Rab’a 1 , Sharifa Al-Sharif 1 and Mohammad Al-Khaleel 1,2, * 1 Department of Mathematics, Yarmouk University, Irbid 21163, Jordan 2 Department of Mathematics, Khalifa University of Science and Technology, Abu Dhabi 127788, United Arab Emirates * Correspondence: mohammad.alkhaleel@ku.ac.ae Abstract: In this paper, we introduce a new approach to solving fractional initial and boundary value problems involving a heat equation, a wave equation, and a telegraph equation by modifying the double Sumudu transform of the fractional type. We discuss a modified double conformable Sumudu transform together with the conditions for its existence. In addition, we prove some more properties of the fractional-type Sumudu transform, including convolution and other properties, which are well known for their use in solving various symmetric and asymmetric problems in applied sciences and engineering. Keywords: conformable fractional derivative; Sumudu transform; convolution 1. Introduction Fractional differential equations appear widely in various applied sciences and en- gineering applications in order to improve the quality of modeling and better describe real-world problems, which include economic, physical, electrical, and biological applica- tions, among many others. One can refer, for instance, to [1] and the references therein, where a good review of the applications of fractional differential equations in economics was given, and to [2] for applications in the circuit domain, in which a time-fractional RC circuit model was considered. Still, a similar fractional mathematical model can be used to better model other types of circuits, such as RLCG circuits, as in [3]. Importantly, an exciting advancement in theoretical physics and nonlinear sciences will be the development of methods for finding the exact solutions of nonlinear partial differential equations that include equations of the fractional type. Such solutions play an important role in the nonlinear sciences, which can lead to further applications. Regarding fractional definitions, in [4], a new fractional definition that was called the conformable fractional derivative was introduced and was defined as follows: For a given function ψ : [0, ∞) −→ R, the conformable fractional derivative of order ϑ is given by D ϑ ψ( x)= lim ε→0 ψ(x+εx 1−ϑ )−ψ(x) ε , ϑ ∈ (0, 1]. This definition is very easy to use when calculating derivatives and solving fractional differential equations compared with other fractional definitions, such as the definitions of Liouville–Riemann and Caputo fractional derivatives. Moreover, one of its most interesting advantages is that it can be easily used to generalize many integral transforms, such as Laplace and Sumudu transforms. Various modifications of the original definition were proposed by many researchers; see, for instance, [5] and the references therein. Recently, several powerful methods have been developed to obtain the exact solutions for conformable fractional partial differential equations, such as the reliable methods in [6,7], the single and double Laplace transform methods in [8–10], and the double Shehu transform in [11]. Symmetry 2022, 14, 2249. https://doi.org/10.3390/sym14112249 https://www.mdpi.com/journal/symmetry