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[null,"1.","Record Nr.",null,"UNINA9910491051203321"]
[null,null,"Titolo",null,"Categorie di pensiero e categorie di lingua : l'idioma filosofico di John Wilkins / Francesca Chiusaroli ; con un'appendice di Angela Longo"]
[null,null,"Pubbl/distr/stampa",null,"Il Calamo"]
[null,null,"Lingua di pubblicazione",null,"Italiano"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,"2.","Record Nr.",null,"UNISA996466475803316"]
[null,null,"Autore",null,"Annaby Mahmoud H"]
[null,null,"Titolo",null,"Q-fractional calculus and equations / / by Mahmoud H. Annaby, Zeinab S. Mansour"]
[null,null,"Pubbl/distr/stampa",null,"Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2012"]
[null,null,"ISBN",null,"3-642-30898-8"]
[null,null,"Edizione",null,"[1st ed. 2012.]"]
[null,null,"Descrizione fisica",null,"1 online resource (xix, 318 pages) : illustrations"]
[null,null,"Collana",null,"Lecture Notes in Mathematics, , 0075-8434 ; ; 2056"]
[null,null,"Disciplina",null,"515"]
[null,null,"Soggetti",null,"Fractional calculus"]
[{"$nulls":4},"Difference equations"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references (p. 303-314) and indexes."]
[null,null,"Nota di contenuto",null,"1 Preliminaries -- 2 q-Difference Equations -- 3 q-Sturm Liouville Problems -- 4 Riemann–Liouville q-Fractional Calculi -- 5 Other q-Fractional Calculi -- 6 Fractional q-Leibniz Rule and Applications -- 7 q-Mittag–Leffler Functions -- 8 Fractional q-Difference Equations -- 9 Applications of q-Integral Transforms."]
[null,null,null,"Sommario/riassunto","This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  q-Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional q-calculi of the types Riemann–Liouville; Grünwald–Letnikov;  Caputo;  Erdélyi–Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications  in q-series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working towards the investigation of q-fractional difference equations; families of q-Mittag-Leffler functions are defined and their properties are investigated, especially the q-Mellin–Barnes integral  and Hankel contour integral representation of  the q-Mittag-Leffler functions under consideration,  the distribution, asymptotic and reality of their zeros, "]
[{"$nulls":4},"establishing q-counterparts of Wiman’s results. Fractional q-difference equations are studied; existence and uniqueness theorems are given and classes of Cauchy-type problems are completely solved in terms of families of q-Mittag-Leffler functions. Among many q-analogs of classical results and concepts, q-Laplace, q-Mellin and q2-Fourier transforms are studied and their applications are investigated."]