Symmetry in Differential Equations and Integral Operators
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".
Deadline for manuscript submissions: 31 August 2024 | Viewed by 2626
Special Issue Editors
Interests: mathematics and computer science
Special Issues, Collections and Topics in MDPI journals
Interests: integral equations in Banach spaces; groups and semigroups of linear operators; qualitative theory of discrete and continuous evolution equations in Banach spaces; Hyers–Ulam stability and its connections with exponential dichotomy; long time behavior for solutions of abstract Cauchy problems in Banach spaces; fixed point theory and its application
Special Issues, Collections and Topics in MDPI journals
Interests: distribution theory; Hankel transform; fractional calculus of generalized functions; integral equations; fractional differential equations with fixed point theories
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
The symmetry of differential equation systems involves a transformation that maps any solution to another solution within the system. For a first-order ODE, the invariance of the ODE under a point symmetry is equivalent to the existence of a first integral for the ODE. However, in general, integral operators are arbitrary to some extent. Indeed, if we have any solution of a linear differential equation which depends on some parameters, then an integral of the solution multiplied by any function of the parameter represents an integral operator, in turn generating solutions of the equation. One could also consider operators which permit the development of a systematic and unified theory of solutions of partial differential equations on the basis of complex function theory. As a result, it seems that a certain type of integral operator is of particular interest for many situations. However, it is also important to study various other types of integral operators since many situations will generate equations where other types of integral operators are applicable and useful. In this SI, we hope to receive papers on the above topics.
[1] Agarwal, Ravi; Hristova, S.; O'Regan, D. Integral representations of scalar delay non-instantaneous impulsive Riemann-Liouville fractional differential equations. Appl. Anal. 101 (2022), no. 18, 6495--6513.
[2] Positive Solutions for a High-Order Riemann-Liouville Type Fractional Integral Boundary Value Problem Involving Fractional Derivatives. By Wuyang Wang, Jun Ye, Jiafa Xu and Donal O’Regan. Symmetry 2022, 14(11), 2320; https://doi.org/10.3390/sym14112320 - 04 Nov 2022.
[3] Jabeen, T.; Agarwal, R. P.; Lupulescu, V.; O'Regan, D. Existence of global solutions for some classes of integral equations; translated from Ukraïn. Mat. Zh. 70 (2018), no. 1, 130--148 Ukrainian Math. J. 70 (2018), no. 1, 142--163.
[4] Chaharpashlou, Reza; Atangana, Abdon; Saadati, Reza. On the fuzzy stability results for fractional stochastic volterra integral equation. Discrete Contin. Dyn. Syst. Ser. S 14 (2021), no. 10, 3529--3539.
[5] Chaharpashlou, R.; O'Regan, Donal; Park, Choonkil; Saadati, Reza. $C^*$-algebra valued fuzzy normed spaces with application of Hyers-Ulam stability of a random integral equation. Adv. Difference Equ. 2020, Paper No. 326, 9 pp.
[6] Murza, Adrian C. Heteroclinic cycles in ODEs with the symmetry of the quaternion $\bold Q_8$ group. Math. Rep. (Bucur.) 22(72) (2020), no. 2, 87--98.
[7] Positive Solutions for a System of Riemann–Liouville Type Fractional-Order Integral Boundary Value Problems. By Keyu Zhang, Fehaid Salem Alshammari, Jiafa Xu and Donal O’Regan. Fractal Fract. 2022, 6(9), 480; https://doi.org/10.3390/fractalfract6090480 - 29 Aug 2022.
[8] Ndogmo, Jean-Claude. Some variational principles associated with ODEs of maximal symmetry. Part 2: the general case. J. Appl. Anal. 24 (2018), no. 2, 175--183.
[9] New Stability Results of an ABC Fractional Differential Equation in the Symmetric Matrix-Valued FBS by Zahra Eidinejad,Reza Saadati,Radko Mesiar and Chenkuan Li. Symmetry 2022, 14(12), 2667; https://doi.org/10.3390/sym14122667 - 16 Dec 2022.
Dr. Reza Sadaati
Prof. Dr. Donal O'Regan
Prof. Dr. Chenkuan Li
Guest Editors
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