Power-type estimates for a nonlinear fractional differential equation

Abstract In this work, we are concerned with a family of nonlinear ordinary differential equations of fractional order. It is proved that solutions of these equations with weighted initial data exist globally and decay as a power function.

[1]  L. Campos ON THE SOLUTION OF SOME SIMPLE FRACTIONAL DIFFERENTIAL EQUATIONS , 1990 .

[2]  W. Okrasinski On a nonlinear convolution equation occurring in the theory of water percolation , 1980 .

[3]  G. Butler,et al.  A generalization of a lemma of Bihari and applications to pointwise estimates for integral equations , 1971 .

[4]  Ahmad Zain,et al.  Local existence theorems for ordinary differential equations of fractional order , 1982 .

[5]  S. Askhabov A System of Inhomogeneous Integral Equations of Convolution Type with Power Nonlinearity , 2023, Siberian Mathematical Journal.

[6]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[7]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[8]  Marek W. Michalski Derivatives of noninteger order and their applications , 1993 .

[9]  A. Kilbas,et al.  On the Solution of Nonlinear Volterra Convolution Equation with Power Nonlinearity , 1996 .

[10]  W. Okrasinski On the existence and uniqueness of non-negative solutions of a certain non-linear convolution equation , 1979 .

[11]  J. Trujillo,et al.  Differential equations of fractional order:methods results and problem —I , 2001 .

[12]  J. Trujillo,et al.  EXISTENCE AND UNIQUENESS THEOREMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS , 2000 .

[13]  Milan Medveď,et al.  A New Approach to an Analysis of Henry Type Integral Inequalities and Their Bihari Type Versions , 1997 .

[14]  I. Podlubny Fractional differential equations , 1998 .

[15]  P. Bushell,et al.  Nonlinear Volterra integral equations and the Apéry identities , 1992 .

[16]  P. Bushell,et al.  On a class of Volterra and Fredholm non-linear integral equations , 1976, Mathematical Proceedings of the Cambridge Philosophical Society.

[17]  Anatoly A. Kilbas,et al.  On solution of integral equation of Abel-Volterra type , 1995, Differential and Integral Equations.

[18]  Stefan Samko,et al.  Upper and Lower Bounds for Solutions of Nonlinear Volterra Convolution Integral Equations with Power Nonlinearity , 2000 .

[19]  W. Schneider The general solution of a non-linear integral equation of convolution type , 1982 .

[20]  Shuqin Zhang,et al.  The Existence of a Positive Solution for a Nonlinear Fractional Differential Equation , 2000 .

[21]  N. Tatar,et al.  Convergence Rates for a Reaction-Diffusion System , 2001 .

[22]  D. Bainov,et al.  Integral Inequalities and Applications , 1992 .

[23]  Matsusaburô Fujiwara,et al.  On the Integration and Differentiation of an Arbitrary Order , 1933 .

[24]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[25]  Luigi Rodino,et al.  Existence and Uniqueness for a Nonlinear Fractional Differential Equation , 1996 .

[26]  Anatoly A. Kilbas,et al.  On Solution of Nonlinear Abel–Volterra Integral Equation☆ , 1999 .

[27]  J. H. Barrett,et al.  Differential Equations of Non-Integer Order , 1954, Canadian Journal of Mathematics.