Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
2 results
Search Results
Article Citation - Scopus: 2Existence of Solutions of Multi-Order Fractional Differential Equations(Elsevier B.V., 2025) Bouchelaghem, F.; Boulares, H.; Ardjouni, A.; Jarad, F.; Abdeljawad, T.; Abdalla, B.; Shah, K.Recently, the field of fractional calculus has garnered significant attention due to its wide range of applications across various disciplines in science and engineering. Numerous results have been derived using tools from numerical functional analysis and fixed point theory to address a variety of problems in this area. This study employs the Banach Fixed Point Theorem (BFPT) to establish the existence and uniqueness of solutions for Riemann–Liouville fractional differential equations (RLFDEs) involving multiple orders. Sufficient conditions for the existence of solutions to the problem under consideration have been provided. Furthermore, an illustrative example is presented to validate the theoretical findings. © 2025Article On Solutions of Variable-Order Fractional Differential Equations(Elsevier B.V., 2017) Akgül, Ali; Inc, Mustafa; Baleanu, Dumitru; Abdalla, Bahaaeldin; Jarad, Fahd; Bouchelaghem, Faycal; Abdeljawad, Thabet; Ardjouni, Abdelouaheb; Boulares, Hamid; Shah, KamalNumerical calculation of the fractional integrals and derivatives is the code tosearch fractional calculus and solve fractional differential equations. The exactsolutions to fractional differential equations are compelling to get in real ap-plications, due to the nonlocality and complexity of the fractional differentialoperators, especially for variable-order fractional differential equations. There-fore, it is significant to enhance numerical methods for fractional differentialequations. In this work, we consider variable-order fractional differential equa-tions by reproducing kernel method. There has been much attention in theuse of reproducing kernels for the solutions to many problems in the recentyears. We give an example to demonstrate how efficiently our theory can beimplemented in practice.