Existence and uniqueness of nonlocal boundary conditions for Hilfer–Hadamard-type fractional differential equations

Advances in Difference Equations

article

Salamooni, Ahmad Y. A.¹  Pawar, D. D.² 

[1] Department of Mathematics, Faculty of Education Zabid, Hodeidah University;School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University

关键词: Existence;    Uniqueness;    Nonlinear boundary value problems;    Hilfer–Hadamard type;    Fractional differential equation and fractional calculus;   

DOI  :  10.1186/s13662-021-03358-0

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we use some fixed point theorems in Banach space for studying the existence and uniqueness results for Hilfer–Hadamard-type fractional differential equations$$ {}_{\mathrm{H}}D^{\alpha ,\beta }x(t)+f\bigl(t,x(t)\bigr)=0 $$ on the interval$(1,e]$ with nonlinear boundary conditions$$ x(1+\epsilon )=\sum_{i=1}^{n-2}\nu _{i}x(\zeta _{i}),\qquad {}_{\mathrm{H}}D^{1,1}x(e)= \sum_{i=1}^{n-2} \sigma _{i}\, {}_{\mathrm{H}}D^{1,1}x( \zeta _{i}). $$.

【 授权许可】

CC BY