Analysis of Q-Fractional Implicit Differential Equation with Nonlocal Riemann-Liouville and Erdelyi-Kober Q-Fractional Integral Conditions

被引：10

作者：

Zada, Akbar ^{[1
]}

Alam, Mehboob ^{[1
]}

Khalid, Khansa Hina ^{[1
]}

Iqbal, Ramsha ^{[1
]}

Popa, Ioan-Lucian ^{[2
]}

机构：

[1] Univ Peshawar, Dept Math, Peshawar, Khyber Pakhtunk, Pakistan

[2] 1 Decembrie 1918 Univ Alba Iulia, Dept Exact Sci & Engn, Alba Iulia 510009, Romania

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2022年 / 21卷 / 03期

关键词：

Fractional q-differential equations; Fixed point theorem; Erdelyi-Kober q-fractional integral conditions; Green function; Ulam-Hyers stability; STABILITY; EXISTENCE;

D O I：

10.1007/s12346-022-00623-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This manuscript aims to present the existence, uniqueness, and various kinds of Ulam's stability for the solution of the implicit q-fractional differential equation corresponding to nonlocal Erdelyi-Kober q-fractional integral conditions. We use different fixed point theorems to obtain the existence and uniqueness of solution. For stability, we utilize the classical technique of nonlinear functional analysis. The examples are presented as applications to illustrate the main results.

引用

页数：39

共 48 条

[11]

[Anonymous], 1999, MATH SCI ENG

[12]

[Anonymous], 2001, Quantum Calculus

[13] On the new fractional hybrid boundary value problems with three-point integral hybrid conditions [J].

Baleanu, D. ;

Etemad, S. ;

Pourrazi, S. ;

Rezapour, Sh. .

ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (01)

[14] A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions [J].

Baleanu, Dumitru ;

Etemad, Sina ;

Rezapour, Shahram .

BOUNDARY VALUE PROBLEMS, 2020, 2020 (01)

[15]

Browder A., 1996, Mathematical Analysis: An Introduction, DOI [10.1007/978-1-4612-0715-3, DOI 10.1007/978-1-4612-0715-3]

[16]

Erdelyi A., 1940, Q. J. Math. os, V11, P212, DOI [10.1093/qmath/os-11.1.212, DOI 10.1093/QMATH/OS-11.1.212]

[17]

Ernst T., 2000, The History of q-Calculus and New Method

[18]

Gaulue L., 2014, REV TECNO CIENTFICA, V6, P77

[19]

Granas A., 2003, Fixed Point Theory, DOI [10.1007/978-0-387-21593-8, DOI 10.1007/978-0-387-21593-8]

[20]

Hale JK., 1993, INTRO FUNCTIONAL DIF, DOI [10.1007/978-1-4612-4342-7, DOI 10.1007/978-1-4612-4342-7]

← 1 2 3 4 5 →