Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions

被引：83
|
作者：
Vivek, D. [1 ]
Kanagarajan, K. [1 ]
Elsayed, E. M. [2 ,3 ]
机构：
[1] Sri Ramakrishna Miss Vidyalaya Coll Arts & Sci, Dept Math, Coimbatore 641020, Tamil Nadu, India
[2] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia
[3] Mansoura Univ, Dept Math, Fac Sci, Mansoura 35516, Egypt
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2018年 / 15卷 / 01期
关键词：
Hilfer fractional derivative; implicit differential equation; fixed point; existence; Ulam stability;
D O I：
10.1007/s00009-017-1061-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this paper is to establish the existence and uniqueness results for implicit differential equations of Hilfer-type fractional order via Schaefer's fixed point theorem and Banach contraction principle. Next, we establish the equivalent mixed-type integral for nonlocal condition. Further we prove the Ulam stability results. The Gronwall's lemma for singular kernels plays an important role to prove our results. We verify our results by providing examples.
引用
收藏
页数：21
相关论文
共 50 条
  • [21] Existence and uniqueness of nonlocal boundary conditions for Hilfer-Hadamard-type fractional differential equations
    Salamooni, Ahmad Y. A.
    Pawar, D. D.
    ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)
  • [22] Stability analysis for fractional order implicit ψ-Hilfer differential equations
    Asma
    Francisco Gomez-Aguilar, Jose
    Rahman, Ghaus Ur
    Javed, Maryam
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (05) : 2701 - 2712
  • [23] Analysis on Controllability Results for Impulsive Neutral Hilfer Fractional Differential Equations with Nonlocal Conditions
    Linitda, Thitiporn
    Karthikeyan, Kulandhaivel
    Sekar, Palanisamy Raja
    Sitthiwirattham, Thanin
    MATHEMATICS, 2023, 11 (05)
  • [24] Existence and Stability Analysis for Fractional Differential Equations with Mixed Nonlocal Conditions
    Asawasamrit, Suphawat
    Nithiarayaphaks, Woraphak
    Ntouyas, Sotiris K.
    Tariboon, Jessada
    MATHEMATICS, 2019, 7 (02)
  • [25] Existence of the mild solution for some fractional differential equations with nonlocal conditions
    Mophou, G. M.
    N'Guerekata, G. M.
    SEMIGROUP FORUM, 2009, 79 (02) : 315 - 322
  • [26] Existence of the mild solution for some fractional differential equations with nonlocal conditions
    G. M. Mophou
    G. M. N’Guérékata
    Semigroup Forum, 2009, 79 : 315 - 322
  • [27] Existence and Uniqueness Results for a Fractional Differential Equations with Nonlocal Boundary Conditions
    Verma, Sachin Kumar
    Vats, Ramesh Kumar
    Nain, Ankit Kumar
    BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2022, 40
  • [28] Existence and stability results for impulsive (k, ψ)-Hilfer fractional double integro-differential equation with mixed nonlocal conditions
    Sudsutad, Weerawat
    Lewkeeratiyutkul, Wicharn
    Thaiprayoon, Chatthai
    Kongson, Jutarat
    AIMS MATHEMATICS, 2023, 8 (09): : 20437 - 20476
  • [29] EXISTENCE AND STABILITY RESULTS FOR NONLINEAR IMPLICIT FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSES
    Benchohra, Mouffak
    Bouriah, Soufyane
    MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2016, 69 : 15 - 31
  • [30] Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations
    Mali, Ashwini D.
    Kucche, Kishor D.
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (15) : 8608 - 8631
12345