New relationships connecting a class of fractal objects and fractional integrals in space

• Published in: Fractional calculus & applied analysis Vol. 16; no. 4; pp. 911 - 936
• Main Authors: Nigmatullin, Raoul R., Baleanu, Dumitru
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.12.2013; Versita
• Subjects: Abstract Harmonic Analysis; Analysis; averaging of smooth functions on spatial fractal sets; Cantor set; Cantor set: fractal object; fractal object; Functional Analysis; Integral Transforms; Mathematics; Mathematics and Statistics; Operational Calculus; Primary 28A80, 26A33; Secondary 60G18, 26A30, 28A78; self-similar object; spatial fractional integral; Survey Paper; Cantor set; Secondary 60G18, 26A30, 28A78; Primary 28A80, 26A33; spatial fractional integral; Cantor set: fractal object; fractal object; averaging of smooth functions on spatial fractal sets; self-similar object
• ISSN: 1311-0454; 1314-2224
• DOI: 10.2478/s13540-013-0056-1

Many specialists working in the field of the fractional calculus and its applications simply replace the integer differentiation and integration operators by their non-integer generalizations and do not give any serious justifications for this replacement. What kind of “Physics” lies in this mathema...