TY - JOUR A1 - Chaudhary, Renu A1 - Diethelm, Kai A1 - Hashemishahraki, Safoura T1 - On the separation of solutions to fractional differential equations of order α ∈ (1, 2) JF - Applied Numerical Mathematics N2 - Given a Caputo-type fractional differential equation with order between 1 and 2, we consider two distinct solutions to this equation subject to different sets of initial conditions. In this framework, we discuss nontrivial upper and lower bounds for the difference between these solutions. The main emphasis is on describing how such bounds are related to the differences of the associated initial values. Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:863-opus-57338 VL - 203 SP - Article No. 38 ER - TY - JOUR A1 - Singh, Vikram A1 - Chaudhary, Renu A1 - Kumar, Umesh A1 - Kumar, Sandeep T1 - Approximate Controllability of Fractional Evolution System on Non-Dense Domain JF - Qualitative Theory of Dynamical Systems N2 - This article explores the existence and approximate controllability of integral solutions for Hilfer fractional evolution equations in a non-dense domain. Leveraging the well-known generalized Banach contraction theorem, we establish both the existence and uniqueness of the integral solution. Furthermore, we adopt a sequential approach to derive results related to approximate controllability, without relying on the compactness of semigroups or the uniform boundedness of nonlinear functions. To validate our findings, we present and discuss an illustrative example. Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:863-opus-57760 SN - 1575-5460 VL - 23 IS - S1 PB - Springer ER - TY - JOUR A1 - Chaudhary, Renu A1 - Diethelm, Kai T1 - Revisiting diffusive representations for enhanced numerical approximation of fractional integrals JF - IFAC-PapersOnLine N2 - This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of fractional integrals. The approach seamlessly aligns with established techniques used in addressing problems involving integer-order operators, contributing to a unified framework for numerical solutions. Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:863-opus-51989 VL - 58 IS - 12 SP - 418 EP - 423 ER - TY - JOUR A1 - Chaudhary, Renu A1 - Diethelm, Kai T1 - Novel variants of diffusive representation of fractional integrals: Construction and numerical computation JF - IFAC-PapersOnLine N2 - In this paper, we revisit the diffusive representations of fractional integrals established in Diethelm (2023a) to explore novel variants of such representations which provide highly efficient numerical algorithms for the approximate numerical evaluation of fractional integrals. Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:863-opus-51975 VL - 58 IS - 12 SP - 412 EP - 417 ER -