Topological degree theory and Caputo–Hadamard fractional boundary value problems

Abstract

We study two hybrid and non-hybrid fractional boundary value problems via the Caputo-Hadamard type derivatives. We seek the existence criteria for these two problems separately. By utilizing the generalized Dhage's theorem, we derive desired results for an integral structure of solutions for the hybrid problems. Also by considering the special case as a non-hybrid boundary value problem (BVP), we establish other results based on the existing tools in the topological degree theory. In the end of the article, we examine our theoretical results by presenting some numerical examples to show the applicability of the analytical findings.

Numerical study of fractional order COVID-19 pandemic transmission model in context of ABO blood group

“…The main causes of utilizing the fractional-order models (FDMs) is linked to frameworks that have history, memory, or effects of non-locality that can be found in several biological paradigms which shows slowly the realistic double phases refusing manner of infection or diseases. It has been investigated in several scientific papers in the literature that the generalization of the mathematical integer order systems by fractional derivative models the natural manner in a very formal technique for instance in the method suggested in [19] by Akbari et al, in [20] , [21] , [22] , [23] , [24] , [25] , [26] , [16] by Etemad et al, in [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] by Baleanu et al, in [36] , [37] by and in [38] by Talaee et al Latterly, several researchers have been issued on the concept of fractional derivative operator called “ Caputo-Fabrizio operator ” (see for instance, [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] ). Different mathematical paradigms are utilized for simulating COVID-19 transition (see for instance, [49] , [50] , [51] , [52] , [53] , [54] , [55] ).…”

Qualitative Study on Solutions of a Hadamard Variable Order Boundary Problem via the Ulam–Hyers–Rassias Stability

“…Although this idea seems elementary and simple, it involves remarkable effects and outcomes which describe many physical and natural phenomena accurately. For this reason, research into both of the theoretical and practical aspects of boundary value problems has attracted the focus of many mathematicians in international academic institutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. A main difference and novelty in this investigation is the application of the concept of variable order operators.…”

An efficient approach for solution of fractional-order Helmholtz equations

“…A significant phenomenon of these evolution equations is that it produces the Brownian fractional movement, a Brownian motion generalization. In several articles and books, different definitions of fractional calculus are available [1][2][3][4][5][6][7][8][9][10].…”