An alternative definition of the fractional in space derivatives

Key Points

• The aim is to propose a new definition for fractional derivatives based on existing theories and methods.
• Developed an alternative definition based on the theory of operational calculus for unbounded operators.
• Analyzed the spectrum of the proposed operator, ensuring it resides within the imaginary axis.
• Presented findings that interpolate between derivatives of varying integer orders.
• Introduced an operator that bridges gaps between different integer-order derivatives.
• Demonstrated theoretical robustness of the new fractional Laplacian operator under analysis.
• Outlined implications for mathematical applications involving fractional calculus.