Pure mathematics

Applied mathematics

Constant coefficients

Dimension (graph theory)

Variable (mathematics)

Economics

Computer science

Differential operator

Thermodynamics

Fractal

Physics

Microlocal analysis

Fourier integral operator

Mathematics

Differential (mechanical device)

Fractal dimension

Mathematical analysis

Programming language

Finance

Fractional calculus

Operator theory

Order (exchange)

Constant (computer programming)

Chaos Solitons & Fractals

The complexities of nature have pushed humankind to construct complex mathematical formula that can be used to capture such natural occurrence. Very recently the concept differential and integral operators with fractional order and fractal dimension were introduced. The concept has opened new doors for investigations. In this paper, we present a step forward, where the constant fractal dimension is replaced by variable dimension. We present in detail some properties of this new operators, we suggested a new numerical approach that can be used to solve differential and integral equations associate to this operators. We presented some examples and simulations are presented to underpin the strength of the new operators. We strongly believe that this paper will open many new doors of investigation toward modeling real world problems.

Differential and integral operators with constant fractional order and variable fractional dimension