A Study of a Fully Coupled Two-Parameter System of Sequential Fractional Integro-Differential Equations with Nonlocal Integro-Multipoint Boundary Conditions

Heymans N, Bauwens J C. Fractal Theological models and fractional differential equations for viscoelastic behavior. Rheologica Acta, 1994, 33: 210–219

Glockle W, Nonnenmacher T. A fractional calculus approach to self-similar protein dynamics. Biophysical Journal, 1995, 68: 46–53

Metzler R, Klafter J. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Physics Reports, 2000. 339: 1–77

Arena P, Fortuna L, Porto D. Chaotic behavior in noninteger-order cellular neural networks. Physical Review E, 2000, 61: 7761–7781

Schumer R, Benson D, Meerschaertb M, Wheatcraft S. Eulerian derivative of the fractional advection-dispersion equation. J Contaminant, 2001, 48: 69–88

Picozzi S, West B J. Fractional Langevin model of memory in financial markets, Physics Review E, 2002, 66: 46–118

Henry B, Wearne S. Existence of Turing instabilities in a two-species fractional reaction-diffusion system. SIAM J Appl Math, 2002, 62: 870–887

Reyes-Melo E, Martinez-Vega J, Guerrero-Salazar C, Ortiz-Mendez U. Application of fractional calculus to the modeling of dielectric relaxation phenomena in polymeric materials. J Appl Phys Sci, 2005, 98: 923–935

Hilfer R. Anomalous transport: Foundations and applications//Klages R, Radons G, Sokolov I M. Anomalous Transport: Foundations and Applications. Wiley-VCH, 2008: 17–74

Lundstrom B, Higgs M, Spain W, Fairhall A. Fractional differentiation by neocortical pyramidal neurons. Nature Neuroscience, 2008, 11: 1335–1342

Matsuzaki T, Nakagawa M. A chaos neuron model with fractional differential equation. J Phys Soc Jpn, 2003, 72: 2678–2684

Magin R L. Fractional Calculus in Bioengineering. Begell House Publishers, 2006

Herrmann R. Fractional Calculus: An Introduction for Physicists. Singapore: World Scientific, 2011

Wang J R, Zhou Y, Feckan M. On the nonlocal Cauchy problem for semilinear fractional order evolution equations. Cent Eur J Math, 2014, 12: 911–922

Henderson J, Kosmatov N. Eigenvalue comparison for fractional boundary value problems with the Caputo derivative. Fract Calc Appl Anal, 2014, 17: 872–880

Castaing C, Truong L X, Phung P D. On a fractional differential inclusion with integral boundary condition in Banach spaces. J Nonlinear Convex Anal, 2016, 17: 441–471

Ahmad B, Ntouyas S K, Tariboon J. A nonlocal hybrid boundary value problem of Caputo fractional integro-differential equations. Acta Mathematica Scientia, 2016, 36B: 1631–1640

Ge Z M, Ou C Y. Chaos synchronization of fractional order modified Duffing systems with parameters excited by a chaotic signal. Chaos Solitons Fractals, 2008, 35: 705–717

Zhang F, Chen G, Li C, Kurths J. Chaos synchronization in fractional differential systems. Phil Trans R Soc, 2013, 371A: 20120155

Ostoja-Starzewski M. Towards thermoelasticity of fractal media. J Thermal Stresses, 2007, 30: 889–896

Povstenko Y Z. Fractional Thermoelasticity. New York: Springer, 2015

Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Amsterdam: Elsevier Science BV, 2006

Diethelm K. The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo Type. Heidelberg: Springer-Verlag, 2010

Ding X L, Nieto J J. Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions. Commun Nonlinear Sci Numer Simul, 2017, 52: 165–176

Ahmad B, Nieto J J, Alsaedi A, Aqlan M H. A coupled system of Caputo-type sequential fractional differential equations with coupled (periodic/anti-periodic type) boundary conditions. Mediterr J Math, 2017, 14: 227

Ahmad B, Ntouyas S K. A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations. Fract Calc Appl Anal, 2014, 17(2): 348–360

Aljoudi S, Ahmad B, Nieto J J, Alsaedi A. On coupled Hadamard type sequential fractional differential equations with variable coefficients and nonlocal integral boundary conditions. Filomat, 2017, 31: 6041–6049

Khalaf S L, Khudair A R. Particular solution of linear sequential fractional differential equation with constant coefficients by inverse fractional differential operators. Differ Equ Dyn Syst, 2017, 25: 373–383

Aljoudi S, Ahmad B, Nieto J J, Alsaedi A. A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions. Chaos Solitons & Fractals, 2016, 91: 39–46

Tariboon J, Ntouyas S K, Sudsutad W. Coupled systems of Riemann-Liouville fractional differential equations with Hadamard fractional integral boundary conditions. J Nonlinear Sci Appl, 2016, 9: 295–308

Ahmad B, Alsaedi A, Aljoudi S, Ntouyas S K. On a coupled system of sequential fractional differential equations with variable coeffcients and coupled integral boundary conditions. Bull Math Soc Sci Math Roumanie (NS), 2017, 60(108): 3–18

Ahmad B, Nieto J J. Boundary value problems for a class of sequential integrodifferential equations of fractional order. J Funct Spaces Appl, 2013, Art ID 149659

Granas A, Dugundji J. Fixed Point Theory. New York: Springer-Verlag, 2003