Analytical Investigation of the Existence of Solutions for a System of Nonlinear Hadamard-Type Integro-Differential Equations Based upon the Multivariate Mittag-Leffler Function

Abstract

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 nonlinear alternative, and the multivariate Mittag-Leffler function. Using an illustrative example, a demonstration of the application of the main theorem is also considered.

Higher Transcendental Functions and Their Multi-Disciplinary Applications

“…The geographical distribution of the contributors to this Special Issue is remarkably widely-scattered. Their contributions (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]) originated in many different countries on every continent of the world.…”

“…The subject matter of the first 16 publications (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]) dealt extensively with analytic, univalent, multivalent, and harmonic functions of complex analysis and their quantum or basic (or q-) extensions, the Euler-Poisson-Darboux partial differential equation, approximation theory and associated summability methods, variational inequalities, linear and nonlinear integro-differential equations, growth results involving Dirichlet series, theory and applications of wavelet transforms, analysis of ordinary and partial differentialdifference equations, and several other topics listed in the preceding section.…”

Mittag-Leffler Functions in the Integral Representation of a Class of FDEs: Existence, Stability and Numirical Study.

“…For more results on the UH stability, the reader can see the papers [1], [6], [26], [36]. Before moving on to explain our proposed work, we cite the research paper [28], where the authors studied the existence of solutions of the following system of nonlinear Hafamard-type integral equations:…”