This study introduces novel generalized fractional derivatives known as $(\psi,\phi)$-fractional derivatives of the Riemann-Liouville and Caputo types, each incorporating exponential function kernels. These new operators offer distinct advantages, including a semi-group property and a seamless extension of the Riemann-Liouville (RL-FD) and Caputo fractional derivatives (C-FD), as well as integrals (RL-FI). We explore the Laplace transform of these $(\psi,\phi)$-fractional derivatives and $(\psi,\phi)$-integral, leveraging them to address linear $(\psi,\phi)$-fractional differential equations. Moreover, these fractional operators are general to classical fractional operators, cotangent fractional operators, and generalized proportional operators.
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