20 Results Found

In this paper, the authors propose an investigation of the existence of solutions for a system of nonlinear Hadamard-type integro-differential equations in a Banach space. The result derived is new and based upon Babenko’s approach, Leray-Schauder’s...

A remarkably large number of unified integrals involving the Mittag–Leffler function have been presented. Here, with the same technique as Choi and Agarwal, we propose the establishment of two generalized integral formulas involving a multivariate ge...

The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It is shown that the fractional derivative and integral operators are bounded. Some fundamental characteristics of the new fractional op...

In the recent era of research, the field of integral inequalities has earned more recognition due to its wide applications in diverse domains. The researchers have widely studied the integral inequalities by utilizing different approaches. In this pr...

The nonlinear Bagley–Torvik equation is of fundamental importance, as it captures a realistic and intricate interplay among memory effects, nonlinearity, and functional dependence—making it a powerful model for a wide range of natural and...

In this article, a novel type of equation, namely the $\mathsf{\Phi }$-Hilfer fractional-order integro-differential delay system ($\mathsf{\Phi }$-HFOIDDS), is proposed. Here, we study the existence and Hyers–Ulam–Mittag–Leffler (H-U-M-L) stability of th...

This paper studies the uniqueness of solutions for several generalized Abel’s integral equations and a related coupled system in Banach spaces. The results derived are new and based on Babenko’s approach, Banach’s contraction principle and the multiv...

The goal of this paper is to study the uniqueness of solutions of several nonlinear Liouville–Caputo integro-differential equations with variable coefficients and initial conditions, as well as an associated coupled system in Banach spaces. The resul...

The current manuscript is concerned with the uniqueness and existence of a solution for a new class of $\Phi$-Hilfer fractional neutral functional integro-differential equations ($\Phi$-HFNFIDEs) with terminal conditions. Firstly, employing Babenko&rsq...

This paper studies the uniqueness of the bounded solution to a new Cauchy problem of the fractional nonlinear partial integro-differential equation based on the multivariate Mittag–Leffler function as well as Banach’s contractive principl...

The harmonic oscillator is a fundamental physical–mathematical system that allows for the description of a variety of models in many fields of physics. Utilizing fractional derivatives instead of traditional derivatives enables the modeling of...

Time-fractional convection–diffusion equations are significant for their ability to model complex transport phenomena that deviate from classical behavior, with numerous applications in anomalous diffusion, memory effects, and nonlocality. This...

The aim of this research article is to use the extended fractional operators involving the multivariate Mittag–Leffler (M-M-L) function, we provide the generalization of the Hermite–Hadamard–Fejer (H-H-F) inequalities. We relate the...

Often referred to as special functions or mathematical functions, the origin of many members of the remarkably vast family of higher transcendental functions can be traced back to such widespread areas as (for example) mathematical physics, analytic...

In this paper, we introduce the matrix Mittag–Leffler function, which is a generalization of the multivariate Mittag–Leffler function, in order to investigate the uniqueness of the solutions to a fractional nonlinear partial integro-diffe...

Several extensions of the classical Mittag-Leffler function, including multi-parameter and multivariate versions, have been used to define fractional integral and derivative operators. In this paper, we consider a function of one variable with five p...

This paper mainly consists of two parts: (i) We study the uniqueness, existence, and stability of a new fractional nonlinear partial integro-differential equation in ${\mathbb{R}}^n$ with three-point conditions and variable coefficients in a Banach space using inv...

This work introduces a new category of proportional fractional integro-differential equations (PFIDEs) governed by functional boundary conditions. We derive verifiable sufficient criteria that guarantee the Ulam–Hyers Stability, existence and u...

This paper develops a generalized Laplace transform theory within weighted function spaces tailored for the analysis of fractional differential equations involving the $\psi$-Hilfer derivative. We redefine the transform in a weighted setting, establis...

Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter α, called the pathway parameter, one can connect generalized type-1 beta family of densities, gene...