Linear first order Riemann-Liouville fractional differential and perturbed Abel's integral equations

被引:17
作者
Lan, Kunquan [1 ]
机构
[1] Ryerson Univ, Dept Math, Toronto, ON M5B 2K3, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Riemann-Liouville fractional differential equations; Perturbed Abel's integral equations; Mean value theorems for fractional derivatives; Equivalence; MULTIPLE POSITIVE SOLUTIONS; BOUNDARY-VALUE PROBLEM; INITIAL-VALUE PROBLEMS; EXISTENCE; UNIQUENESS; OPERATORS; THEOREMS; MODEL;
D O I
10.1016/j.jde.2021.10.025
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Linear first order Riemann-Liouville fractional differential equations are studied. These new equations unify and generalize the Riemann-Liouville, modified Caputo and Caputo fractional differential equations. The equivalences between the fractional differential equations and the corresponding perturbed Abel's inte-gral equations are obtained. These results are useful not only to study the initial or boundary value problems for nonlinear first order Riemann-Liouville fractional differential equations but also to study the solutions of the perturbed Abel's integral equations arising in a problem of mechanics and many other physical prob-lems. The well-known Tonelli's result on solvability of the Abel's integral equation is generalized. We exhibit that there are nonconstant equilibria for some first order Caputo fractional equations. This is dif-ferent from nonlinear first order ordinary differential equations which have only constant equilibria. The equivalence results are applied to generalize the classical Mean Value Theorem to the first order Riemann-Liouville fractional derivatives. (c) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页码:28 / 59
页数:32
相关论文
共 61 条
  • [1] ALBASSAM MA, 1965, J REINE ANGEW MATH, V218, P70
  • [2] Almuthaybiri Saleh S., 2019, Analysis, V39, P117, DOI 10.1515/ anly- 2019-0027.
  • [3] [Anonymous], 1964, Generalized Functions. Volume I: Properties and Operations
  • [4] [Anonymous], 1991, ABEL INTEGRAL EQUATI
  • [5] Bachar I, 2017, ELECTRON J DIFFER EQ
  • [6] Positive solutions for boundary value problem of nonlinear fractional differential equation
    Bai, ZB
    Lü, HS
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 311 (02) : 495 - 505
  • [7] INTEGRAL AND FRACTIONAL EQUATIONS, POSITIVE SOLUTIONS, AND SCHAEFER'S FIXED POINT THEOREM
    Becker, L. C.
    Burton, T. A.
    Purnaras, I. K.
    [J]. OPUSCULA MATHEMATICA, 2016, 36 (04) : 431 - 458
  • [8] BLANK L, 1996, 287 MANCH CTR COMP M
  • [9] Caputo M., 1971, Rivista del Nuovo Cimento, V1, P161, DOI 10.1007/BF02820620
  • [10] LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOST FREQUENCY INDEPENDENT-2
    CAPUTO, M
    [J]. GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1967, 13 (05): : 529 - &