A generalized Lyapunov's inequality for a fractional boundary value problem

We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunovs inequality. The new results are illustrated through examples.

[1]  R. Ferreira.  A Lyapunov-type inequality for a fractional boundary value problem , 2013 .

[2]  Nan Li,et al.  NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS , 2013 .

[3]  H. Kober.  ON FRACTIONAL INTEGRALS AND DERIVATIVES , 1940 .

[4]  Zhitao Chuang,et al.  On equivalent conditions of two sequences to be R-dual , 2015 .

[5]  A. Liapounoff,et al.  Problème général de la stabilité du mouvement , 1907 .

[6]  C. Bai,et al.  Lyapunov-type inequality for a fractional differential equation with fractional boundary conditions , 2015 .

[7]  Xingqiu Zhang,et al.  Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter , 2014, Appl. Math. Comput..

[8]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

[9]  R. Ferreira.  On a Lyapunov-type inequality and the zeros of a certain Mittag–Leffler function , 2014 .

[10]  G. Guseinov,et al.  On the existence of positive solutions for nonlinear differential equations with periodic boundary conditions , 2001 .

[11]  M. Jleli,et al.  A Lyapunov-Type Inequality for a Fractional Differential Equation under a Robin Boundary Condition , 2015 .

[12]  W. Rudin.  Real and complex analysis, 3rd ed. , 1987 .

[13]  Masato Hashizume.  Minimization problem related to a Lyapunov inequality , 2015 .

[14]  D. O’Regan,et al.  Lyapunov-type inequalities for a class of fractional differential equations , 2015 .

[15]  T. Sun,et al.  Lyapunov Inequality For Dynamic Equation With Order n +1 On Time Scales , 2015 .

[16]  M. Jleli,et al.  Lyapunov-type inequalities for fractional boundary value problems , 2019, Fractional Differential Equations.

[17]  W. Rudin.  Real and complex analysis , 1968 .

[18]  M. Jleli,et al.  Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions , 2015 .

[19]  Tingting Qiu,et al.  Positive solutions for boundary value problem of nonlinear fractional differential equation. , 2008 .