Stability analysis of solutions and existence theory of fractional Lagevin equation

Abstract The present article describes fractional Langevin equations (FDEs) invloving Caputo Hadamard-derivative of independent orders connected with non-local integral and non-periodic boundary conditions. The stability, existence, and uniqueness (EU) of solutions for the prescribed equations are defined. Our viewpoint is built on the specification of the Krasnoselskii fixed point theorem and the Banach contraction mapping principle. An application is offered to smooth the comprehension of the hypothetical outcomes.

[1]  H. Mohammadi,et al.  On a hybrid fractional Caputo–Hadamard boundary value problem with hybrid Hadamard integral boundary value conditions , 2020 .

[2]  S. Ntouyas,et al.  Systems of generalized Sturm-Liouville and Langevin fractional differential equations , 2017 .

[3]  D. Baleanu,et al.  Two sequential fractional hybrid differential inclusions , 2020 .

[4]  B. Ahmad,et al.  Impulsively hybrid fractional quantum Langevin equation with boundary conditions involving Caputo qk-fractional derivatives , 2016 .

[5]  T. Abdeljawad,et al.  EXISTENCE AND STABILITY ANALYSIS OF SOLUTIONS FOR FRACTIONAL LANGEVIN EQUATION WITH NONLOCAL INTEGRAL AND ANTI-PERIODIC-TYPE BOUNDARY CONDITIONS , 2020 .

[6]  R. Kubo.  Statistical Physics II: Nonequilibrium Statistical Mechanics , 2003 .

[7]  A. Zada,et al.  Hyers–Ulam stability of nonlinear differential equations with fractional integrable impulses , 2017 .

[8]  Ahmed Alsaedi,et al.  A study of nonlinear Langevin equation involving two fractional orders in different intervals , 2012 .

[9]  Existence of solutions for fractional Langevin equation involving generalized Caputo derivative with periodic boundary conditions , 2020 .

[10]  F. Mainardi.  Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models , 2010 .

[11]  H. Baghani,et al.  A coupled system of Langevin differential equations of fractional order and associated to antiperiodic boundary conditions , 2020 .

[12]  Xuezhu Li,et al.  Ulam-Hyers stability of fractional Langevin equations , 2015, Appl. Math. Comput..

[13]  D. Baleanu,et al.  On a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions by using three operators , 2020 .

[14]  A. Zada,et al.  Stability analysis of nonlinear fractional differential equations with Caputo and Riemann-Liouville derivatives , 2018, The European Physical Journal Plus.

[15]  R. Kubo.  The fluctuation-dissipation theorem , 1966 .

[16]  Dumitru Baleanu,et al.  On Caputo modification of the Hadamard fractional derivatives , 2014, Advances in Difference Equations.

[17]  D. Baleanu,et al.  Spline collocation methods for systems of fuzzy fractional differential equations , 2020 .

[18]  On the oscillation of Hadamard fractional differential equations , 2018, Advances in Difference Equations.

[19]  D. Baleanu,et al.  Collocation methods for terminal value problems of tempered fractional differential equations , 2020 .

[20]  T. Abdeljawad,et al.  Existence results in Banach space for a nonlinear impulsive system , 2019, Advances in Difference Equations.

[21]  D. Lemons,et al.  Paul Langevin’s 1908 paper “On the Theory of Brownian Motion” [“Sur la théorie du mouvement brownien,” C. R. Acad. Sci. (Paris) 146, 530–533 (1908)] , 1997 .

[22]  Ming Li,et al.  Langevin equation with two fractional orders , 2008 .

[23]  D. Baleanu,et al.  On stability analysis and existence of positive solutions for a general non-linear fractional differential equations , 2020 .

[24]  Omid Baghani,et al.  On fractional Langevin equation involving two fractional orders , 2017, Commun. Nonlinear Sci. Numer. Simul..

[25]  Muhammad Aslam,et al.  Existence of positive solution and Hyers–Ulam stability for a nonlinear singular-delay-fractional differential equation , 2019, Advances in Difference Equations.

[26]  Dumitru Baleanu,et al.  Caputo-type modification of the Hadamard fractional derivatives , 2012, Advances in Difference Equations.

[27]  On a fractional hybrid version of the Sturm–Liouville equation , 2020 .

[28]  M. Toda,et al.  In: Statistical physics II , 1985 .

[29]  Dumitru Baleanu,et al.  New fractional signal smoothing equations with short memory and variable order , 2020 .

[30]  Shurong Sun,et al.  Existence of solutions for fractional Langevin equation with infinite-point boundary conditions , 2017 .

[31]  A. Alsaedi,et al.  On a nonlocal integral boundary value problem of nonlinear Langevin equation with different fractional orders , 2019, Advances in Difference Equations.

[32]  Juan J. Nieto,et al.  Fractional Langevin equation with anti-periodic boundary conditions , 2018, Chaos, Solitons & Fractals.

[33]  D. Baleanu,et al.  System of fractional differential algebraic equations with applications , 2019, Chaos, Solitons & Fractals.

[34]  J. F. Gómez‐Aguilar,et al.  Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel , 2019, Chaos, Solitons & Fractals.

[35]  Aziz Khan,et al.  On Coupled p-Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions , 2017, Complex..

[36]  H. Ghaffarzadeh,et al.  Spline collocation methods for seismic analysis of multiple degree of freedom systems with visco-elastic dampers using fractional models , 2020 .

[37]  J. F. Gómez‐Aguilar,et al.  Stability analysis for fractional order advection–reaction diffusion system , 2019, Physica A: Statistical Mechanics and its Applications.

[38]  Liu Yang,et al.  On fractional Langevin differential equations with anti-periodic boundary conditions , 2017 .

[39]  D. H. Hyers.  On the Stability of the Linear Functional Equation. , 1941, Proceedings of the National Academy of Sciences of the United States of America.

[40]  S. Rezapour,et al.  On a hybrid inclusion problem via hybrid boundary value conditions , 2020 .

[41]  J. Alzabut,et al.  A coupled system of nonlinear Caputo–Hadamard Langevin equations associated with nonperiodic boundary conditions , 2020, Mathematical Methods in the Applied Sciences.

[42]  S. Rezapour,et al.  Approximate solutions for a fractional hybrid initial value problem via the Caputo conformable derivative , 2020 .

[43]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .