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Browsing by Author "Sadek, Lakhlifa"

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    The General Caputo-Katugampola Fractional Derivative and Numerical Approach for Solving the Fractional Differential Equations
    (Elsevier, 2025) Sadek, Lakhlifa; Ldris, Sahar Ahmed; Jarad, Fahd
    In this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the psi-Caputo-Katugampola fractional derivative (psi-CKFD). The Caputo-Katugampola (CKFD), the Caputo (CFD), and the Caputo-Hadamard FD (CHFD) are all special cases of this new fractional derivative. We also introduce the psi-Katugampola fractional integral (psi-KFI) and discuss several related theorems. An existence and uniqueness theorem for a psi-Caputo-Katugampola fractional Cauchy problem (psi-CKFCP) is established. Furthermore, we present an adaptive predictor-corrector algorithm for solving the psi-CKFCP. We include examples and applications to illustrate its effectiveness. The derivative used in our approach is significantly influenced by the parameters delta, gamma, and the function psi, which makes it a valuable tool for developing fractional calculus models.