OICC Press Journal of Theoretical and Applied Physics 2251-7235 19 2 2025 04 10 A novel approach to fractional calculus and its applications to well-known problems 1 6 10.57647/j.jtap.2025.1902.16 EN Abdessamad Ait Brahim Department of Mathematics, Sultan Moulay Slimane University, Morocco https://orcid.org/0009-0009-9451-3926 Khalid Hilal Department of Mathematics, Sultan Moulay Slimane University, Morocco https://orcid.org/0000-0002-0806-2623 Abdelmajid El Hajaji OEE Departement, ENCGJ, University of Choaib Doukali, El Jadida, Morroco https://orcid.org/0000-0002-0218-8751 Jalila El Ghordaf Department of Mathematics, Sultan Moulay Slimane University, Morocco Eman Abuteen Department of Basic scientific Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Jordan https://orcid.org/0000-0003-1425-9454 Journal Article 2025 04 10 This paper introduces a novel definition of fractional derivatives and fractional integrals using the conformable derivative approach. This new framework not only aligns more closely with the classical concept of derivatives but also provides a more practical and intuitive structure for fractional calculus. The proposed definition is applicable in two key ranges: 0 ≤ α < 1 and n−1 ≤ α < n, where n is a positive integer. We also demonstrate that when α =1, our definition seamlessly corresponds to the classical first-order derivative. The advantages of this approach include improved compatibility with classical calculus and enhanced computational convenience, making it a valuable tool for both theoretical investigations and practical applications. By bridging fractional calculus with traditional derivative concepts, our definition facilitates easier analysis and interpretation of fractional differential equations and their solutions. We further explore the implications of this definition in various contexts, including its impact on stability and convergence properties in numerical methods, and provide examples to illustrate its effectiveness and applicability.