Kirtiwant P. Ghadle

This paper establishes the existence and uniqueness of solutions for a class of implicit fractional Volterra–Fredholm integrodifferential equations with finite delay and instantaneous impulses. By employing the Banach contraction principle and Schaefer’s fixed‐point theorem, we provide a rigorous analytical foundation for our results. Furthermore, through illustrative examples and numerical simulations, we validate our theoretical findings, which provide a deeper understanding of the problem’s behavior for researchers. Our work not only advances the theoretical framework of impulsive fractional dynamic systems but also provides practical tools for further exploration in applied mathematics and related fields.

In this study, we explore the solutions of fractional differential equations (FDEs) involving the Atangana–Baleanu–Caputo derivative, subject to both integral and impulsive implicit boundary conditions. To establish the existence and uniqueness of solutions, we utilize the Banach Contraction Mapping Principle and Krasnoselskiis fixed point theorem. The Banach principle helps demonstrate the uniqueness by showing the mapping is a contraction under suitable conditions, while Krasnoselskiis theorem is applied to confirm the existence of solutions without requiring strict contraction. An illustrative example is provided to support the theoretical results, demonstrating how the applied methods effectively guarantee the solvability of the given fractional boundary value problem. The example also highlights the practical relevance of the theoretical framework developed. This approach contributes to the broader understanding of FDEs, especially those modeled with nonlocal and impulsive implicit conditions, which are increasingly important in various scientific and engineering applications.

The purpose of this paper is to investigate, the existence and uniqueness of solutions for nonlinear fractional impulsive fractional Volterra–Fredholm integro-differential equations of the Caputo–Hadamard type, with a new modeling integral boundary value problem. The Krasnoselskii fixed-point theorem, Schaefer’s fixed point theorem, and the Banach contraction principle serve as the basis of this unique strategy and are used to achieve the desired results. An example illustrates the theoretical findings.

This paper concentrates on an analytical approach for solving two-dimensional problems of elasticity and thermoelasticity in an inhomogeneous strip in terms of stresses for orthotropic material. Application of direct integration method reduces the differential and compatibility equations in terms of stresses to the integro-differential equation of the second kind. We have solved these dominant equations by applying resolvent kernel technique.

This paper employ an analytical approach for solving the two-dimensional problems of elasticity and thermo-elasticity in terms of stresses in an inhomogeneous strip which is infinite. We consider application of direct integration method in a plane steady state heat conduction problem for a semi plane. Application of this method are depend on the direct integration of equilibrium equation for efficient analysis of inhomogeneous solids. With the application of direct integration method for differential and compatibility equation for isotropic material, we are reducing desired equation to integro-differential equation. We have solved these dominant equations by applying simple iteration method.The results for displacement and stresses are computed numerically. One can find the displacement in terms of strains by the integration of Cauchy relations. Using Simple iteration method to find thermal stresses in terms of Volterra- integro differential equations.The calculation to construct the solution can be also useful to solve some optimization problem as well as inverse thermoelasticity problems in terms of stresses.

In this paper, we will introduce a well-known transformation technique, the modified α-fractional differential transform, to the differential equation of fractional order. We derive some new results with proof using new techniques that never existed before. By using this new technique, we are attempting to solve the nonlinear fractional-order mathematical epidemic model. Furthermore, the fractional epidemic model’s solution obtained by using this new technique is correlated with the solution of the same model calculated for a different fractional order by the modified α-fractional differential transform method. Moreover, using the Python software, we can numerically and graphically represent the solution of fractional differential equations.

The aim of this paper is to study to fractional calculus for class of Ψ function. The present study is designed to study generalized fractional derivatives and find their generalized transforms called Ψ-Laplace transform and Ψ-Sumudu transform. Moreover, find the analytical solutions of some applications in physics the form of generalized fractional derivatives by transform technique

In this paper, we discuss the relationship between Wjkhi and Pjkhi in generalized recurrent and birecurrent Finsler space. Further, we obtain the condition for

This paper deals with study of the plane elasticity of thermoelastic problems for inhomogenous strip. Here, the original problems are reduced to set the governing equations in the volterra integral equations by making the use of direct integration method. Further using the iteration technique the numerical calculations has been performed. The stress distribution obtained and calculated numerically and shown graphically.