Article

Analytical Representation and Applications of Solutions to a Loaded Fractional Integro-Differential Equation

Umida BaltaevaDepartment of Applied Mathematics, Urgench State University, Urgench 220100, UzbekistanBobur KhasanovDepartment of Exact Sciences, Khorezm Mamun Academy, Khiva 220900, UzbekistanHamrobek HayitbayevDepartment of Accounting and General Professional Sciences, Mamun University, Khiva 220900, UzbekistanJamol I. BaltaevDepartment of Technology, RANCH University of Technology, Urgench 220100, UzbekistanYolqin AlikulovDepartment of High Mathematics, Tashkent University of Information Technologies Named after Muhammad Al-Khwarizmi, Tashkent 100084, Uzbekistan

Dynamicsjournal2026en

ABI

Abstract

We study the Cauchy problem for a loaded fractional integro-differential equation with a time-dependent diffusion coefficient. By reducing the problem to an equivalent Volterra integral equation of the second kind, we derive explicit analytical representations of solutions under appropriate regularity assumptions. The construction of the associated resolvent kernel allows us to establish existence and uniqueness results and to investigate the role of the fractional order and the loading term in the solution structure. Two illustrative examples are presented to demonstrate the applicability of the proposed approach.

Topics

Fractional Differential Equations Solutions Nonlinear Differential Equations Analysis Differential Equations and Boundary Problems

Identifiers

DOI: 10.3390/dynamics6010007

Citations and references

Cited by 00 references

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