Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena

J.R. Kantor, The Scientific Evolution of Psychology (Principia Press, Chicago, 1963)

P. Green, Alexander of Macedon (University of California Press Ltd., Oxford, 1991)

R. Sorabji (Editor), Aristotle Transformed (Bloomsburg Academic, London, 1990)

J. Filonik, Athenian Impiety Trials: A Reappraisal (Dike, 2013)

A.G. Kurosh, Mat. Sbornik. 20, 237 (1947)

D. Eisenhardt, Learn Mem. 21, 534 (2014)

I. Yaglom, Complex Numbers in Geometry (Academic Press, N.Y., 1968) pp. 195-219, translated by E. Primrose from 1963 Russian original, appendix: Non-Euclidean geometries in the plane and complex numbers

J. Briggs, Fractals: The Patterns of Chaos (Thames and Hudson, London, 1992)

T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore/New Jersey, 1992)

H. Takayasu, Fractals in the Physical Sciences (Manchester University Press, Manchester, 1990)

R.D. Knight, J. Geom. 83, 137 (2005)

W. Blaschke, Differentialgeometrie der Kreise und Kugeln, in Vorlesungen über Differentialgeometrie, Grundlehren der Mathematischen Wissenschaften (Springer, Berlin, 1929)

M.D. Ortigueira, J.A.T. Machado, J. Comput. Phys. 293, 4 (2015)

V.E. Tarasov, Nonlinear Sci. Numer. Simul. 18, 2945 (2013)

G.B. Folland, Advanced Calculus (Prentice Hall, 2002)

M. Caputo, Geophys. J. Int. 13, 529 (1967)

A. Atangana, B. Dumitru, Therm. Sci. 20, 763 (2016)

M. Caputo, M. Fabrizio, Progr. Fract. Differ. Appl. 2, 1 (2016)

C.G. Galizia, S.L. McIlwrath, R. Menzel, Cell Tissue Res. 295, 383 (1999)

R.D. Schafer, An Introduction to Nonassociative Algebras, Vol. 22 (Academic Press, 1966)

S. Okubo, Introduction to Octonion and Other Non-associative Algebras in Physics (Cambridge University Press, 1995)

E.T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, with an Introduction to the Problem of Three Bodies, 4th ed. (Dover Publications, New York, 1937)

R. Broucke, Astrophys. Space Sci. 72, 33 (1980)

A. Biswas, V. Shapiro, Graph. Models 66, 133 (2004)

F. Cantrijn, A. Ibort, M. De-Leon, J. Aust. Math. Soc. A 66, 303 (1999)

J. Baez, A. Hoffnung, C. Rogers, Commun. Math. Phys. 293, 701 (2010)

K.C. Louden, Compiler Construction: Principles and Practice (1997)

M. Pitkänen, Prespacetime J. 7, 66 (2016)

H. Couclelis, N. Gale, Geogr. Ann. Ser. B Human Geogr. 68, 1 (1986)

M. Chaichian, P. Presnajder, A. Tureanu, Phys. Rev. Lett. 94, 151602 (2005)

S. Doplicher, K. Fredenhagen, J.E. Roberts, Commun. Math. Phys. 172, 187 (1995)

M.R. Douglas, N.A. Nekrasov, Rev. Mod. Phys. 73, 977 (2001)

V. Moretti, Rev. Math. Phys. 15, 1171 (2003)

W. Heisenberg, Z. Phys. 43, 172 (1927)

L.A. Rozema, A. Darabi, D.H. Mahler, A. Hayat, Y. Soudagar, A.M. Steinberg, Phys. Rev. Lett. 109, 100404 (2012)

D.J. Gross, F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973)

R. Gorenflo, J. Loutchko, Y. Luchko, Fract. Calc. Appl. Anal. 5, 491 (2002)

R.N. Pillai, Ann. Inst. Stat. Math. 42, 157 (1990)

C.S. Kumar, B.U. Nair, J. Stat. Appl. 6, 23 (2011)

C.S. Kumar, B.U. Nair, OPSEARCH 52, 86 (2015)

A.M. Mathai, P. Moschopoulos, J. Stat. Appl. Prob. 1, 15 (2012)

J. Hristov, Derivatives with non-singular kernels from the Caputo-Fabrizio definition and beyond: Appraising analysis with emphasis on diffusion models, in Frontiers in Fractional Calculus (Bentham Science Publishers, 2017) pp. 235--295

J. Hristov, Electrical Circuits of Non-integer Order: Introduction to an Emerging Interdisciplinary Area with Examples, in Analysis and Simulation of Electrical and Computer Systems (Springer, 2018) pp. 251--273

A. Atangana, I. Koca, Chaos, Solitons Fractals 89, 447 (2016)

J. Hristov, Therm. Sci. 21, 827 (2016)

B.S.T. Alkahtani, Chaos, Solitons Fractals 89, 547 (2016)

V.F. Morales-Delgado, J.F. Gómez-Aguilar, M.A. Taneco-Hernández, Eur. Phys. J. Plus 132, 527 (2017)

J.F. Gómez-Aguilar, J. Math. Sociol. 41, 172 (2017)

J.F. Gómez-Aguilar, Chaos, Solitons Fractals 95, 179 (2017)

A.A. Tateishi, H.V. Ribeiro, E.K. Lenzi, Front. Phys. 5, 52 (2017)

I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Academic Press, New York, 1998)

L. Changpin, T. Chunxing, Comput. Math. Appl. 58, 1573 (2009)

K. Diethelm, N.J. Ford, A.D. Freed, Numer. Algorithms 36, 31 (2004)

M. Caputo, M. Fabricio, Progr. Fract. Differ. Appl. 1, 73 (2015)

A. Atangana, J.J. Nieto, Adv. Mech. Eng. 7, 1 (2015)

J.F. Gómez-Aguilar, Numer. Methods Part. Differ. Equ. (2017) https://doi.org/10.1002/num.22219

A.M.A. El-Sayed, A.E.M. El-Mesiry, H.A.A. El-Saka, Appl. Math. Lett. 20, 817 (2007)

J.G. Lu, Chaos, Solitons Fractals 26, 1125 (2005)

D.R. Willé, C.T. Baker, Appl. Numer. Math. 9, 223 (1992)

V. Daftardar-Gejji, Y. Sukale, S. Bhalekar, Fract. Calc. Appl. Anal. 18, 400 (2015)

A. Atangana, J.F. Gómez-Aguilar, Numer. Methods Part. Differ. Equ. (2017) https://doi.org/10.1002/num.22195

A. Atangana, E.F. Doungmo-Goufo, Therm. Sci. 19, 231 (2015)